Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation
We develop a notion of nonlinear expectation– G -expectation–generated by a nonlinear heat equation with infinitesimal generator G . We first study multi-dimensional G -normal distributions. With this nonlinear distribution we can introduce our G -expectation under which the canonical process is a m...
Uloženo v:
| Vydáno v: | Stochastic processes and their applications Ročník 118; číslo 12; s. 2223 - 2253 |
|---|---|
| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Amsterdam
Elsevier B.V
01.12.2008
Elsevier |
| Edice: | Stochastic Processes and their Applications |
| Témata: | |
| ISSN: | 0304-4149, 1879-209X |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | We develop a notion of nonlinear expectation–
G
-expectation–generated by a nonlinear heat equation with infinitesimal generator
G
. We first study multi-dimensional
G
-normal distributions. With this nonlinear distribution we can introduce our
G
-expectation under which the canonical process is a multi-dimensional
G
-Brownian motion. We then establish the related stochastic calculus, especially stochastic integrals of Itô’s type with respect to our
G
-Brownian motion, and derive the related Itô’s formula. We have also obtained the existence and uniqueness of stochastic differential equations under our
G
-expectation. |
|---|---|
| AbstractList | We develop a notion of nonlinear expectation-G-expectation-generated by a nonlinear heat equation with infinitesimal generator G. We first study multi-dimensional G-normal distributions. With this nonlinear distribution we can introduce our G-expectation under which the canonical process is a multi-dimensional G-Brownian motion. We then establish the related stochastic calculus, especially stochastic integrals of Itô's type with respect to our G-Brownian motion, and derive the related Itô's formula. We have also obtained the existence and uniqueness of stochastic differential equations under our G-expectation. We develop a notion of nonlinear expectation– G -expectation–generated by a nonlinear heat equation with infinitesimal generator G . We first study multi-dimensional G -normal distributions. With this nonlinear distribution we can introduce our G -expectation under which the canonical process is a multi-dimensional G -Brownian motion. We then establish the related stochastic calculus, especially stochastic integrals of Itô’s type with respect to our G -Brownian motion, and derive the related Itô’s formula. We have also obtained the existence and uniqueness of stochastic differential equations under our G -expectation. |
| Author | Peng, Shige |
| Author_xml | – sequence: 1 givenname: Shige surname: Peng fullname: Peng, Shige email: peng@sdu.edu.cn organization: Institute of Mathematics, Shandong University, 250100, Jinan, China |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=20956329$$DView record in Pascal Francis http://econpapers.repec.org/article/eeespapps/v_3a118_3ay_3a2008_3ai_3a12_3ap_3a2223-2253.htm$$DView record in RePEc |
| BookMark | eNp9kUtv1DAUhS1UJKYtP4BdNiwz-JXEFiuoaKlU6Iaq7Kw79o3qUcaJ7ExL_z03CuqCRRd-Hd3v2D73lJ2kMSFjHwTfCi7aT_ttmWArOe_ovOWiecM2wnS2ltz-PmEbrriutdD2HTstZc85F1KKDbv_cRzmWId4wFTimGCoruqveXxKEVJ1GGfSKkihyjjAjKEq8-gfoMzRVx4GfxyOpTqmgJk4_DOhn2FhztnbHoaC7_-tZ-zu8tuvi-_1ze3V9cWXm9rrVs916IPZcREsqtCp0HBhWwNhZ4zWnbBm12DbCJAKuBfWt53spQ6d1Ts00BlQZ-zn6puR7nZTjgfIzw4RKY9pKu7RKRDC0PxMgwJatnERJU3TokmpnJSNcg_zgQw_roYTFPpgnyH5WF6MKc6mVdJSnVjrfB5Lydi_lAjulpa4vaMnuKUli0QtIab7j_FxjWvOEIdXyc8riZTlY8Tsio-YPIaYKXIXxvgK_RcbBqgB |
| CODEN | STOPB7 |
| CitedBy_id | crossref_primary_10_1016_j_jmaa_2024_128388 crossref_primary_10_1016_j_spa_2020_06_002 crossref_primary_10_1080_03610926_2022_2071448 crossref_primary_10_1080_03610926_2021_1883654 crossref_primary_10_1080_03610926_2023_2258428 crossref_primary_10_1007_s00028_024_01046_6 crossref_primary_10_3390_math13183034 crossref_primary_10_1016_j_jkss_2018_12_002 crossref_primary_10_1155_2019_3695869 crossref_primary_10_3934_puqr_2021001 crossref_primary_10_1016_j_neucom_2022_10_065 crossref_primary_10_1109_ACCESS_2021_3064844 crossref_primary_10_1016_j_jmaa_2020_124342 crossref_primary_10_1155_2021_6611237 crossref_primary_10_1007_s11118_010_9185_x crossref_primary_10_1016_j_spa_2011_03_009 crossref_primary_10_1080_03610926_2024_2430734 crossref_primary_10_1155_2021_6653435 crossref_primary_10_1080_03610926_2020_1790603 crossref_primary_10_1155_2013_342038 crossref_primary_10_1177_0037549717720024 crossref_primary_10_1007_s10959_012_0471_y crossref_primary_10_3390_math11163494 crossref_primary_10_1155_2013_398750 crossref_primary_10_1155_2014_786391 crossref_primary_10_1214_15_AAP1130 crossref_primary_10_1515_rose_2024_2005 crossref_primary_10_1007_s10473_022_0203_z crossref_primary_10_1007_s40304_022_00294_7 crossref_primary_10_1016_j_spa_2013_03_022 crossref_primary_10_1007_s00245_019_09583_0 crossref_primary_10_1016_j_jmaa_2022_126090 crossref_primary_10_1007_s10959_023_01298_x crossref_primary_10_1007_s11766_021_3882_7 crossref_primary_10_3934_puqr_2021013 crossref_primary_10_1007_s00013_016_1002_3 crossref_primary_10_1016_j_apnum_2021_03_012 crossref_primary_10_1155_2019_9037258 crossref_primary_10_1007_s11401_018_0116_2 crossref_primary_10_1016_j_spa_2019_03_014 crossref_primary_10_3934_puqr_2021009 crossref_primary_10_1007_s00780_016_0320_4 crossref_primary_10_1016_j_najef_2021_101634 crossref_primary_10_1007_s00245_020_09716_w crossref_primary_10_1080_03610926_2018_1429632 crossref_primary_10_1515_ijnsns_2021_0479 crossref_primary_10_1007_s11425_018_9558_1 crossref_primary_10_1016_j_cam_2015_10_034 crossref_primary_10_1080_03610926_2022_2051050 crossref_primary_10_1007_s11464_022_1026_x crossref_primary_10_1016_j_na_2012_08_002 crossref_primary_10_1515_rose_2024_2021 crossref_primary_10_1007_s40304_023_00344_8 crossref_primary_10_1002_mma_8121 crossref_primary_10_1007_s10114_015_3212_1 crossref_primary_10_1007_s10255_015_0477_1 crossref_primary_10_1137_S0040585X97T991416 crossref_primary_10_1002_oca_2814 crossref_primary_10_1080_03610926_2022_2028840 crossref_primary_10_1080_07362994_2013_776881 crossref_primary_10_3934_puqr_2021018 crossref_primary_10_1080_07362994_2014_964870 crossref_primary_10_1016_j_spa_2024_104354 crossref_primary_10_1016_j_ejcon_2023_100940 crossref_primary_10_5269_bspm_62304 crossref_primary_10_1016_j_sysconle_2024_105988 crossref_primary_10_1007_s13398_019_00757_7 crossref_primary_10_1080_00207179_2020_1775307 crossref_primary_10_1080_00207721_2018_1551973 crossref_primary_10_1016_j_spa_2009_05_010 crossref_primary_10_1007_s10114_011_0281_7 crossref_primary_10_1080_00207179_2017_1328745 crossref_primary_10_1002_oca_3223 crossref_primary_10_1007_s11766_019_3622_4 crossref_primary_10_1002_oca_2012 crossref_primary_10_1080_00207179_2019_1575527 crossref_primary_10_1080_03610926_2021_1873380 crossref_primary_10_1007_s00362_025_01705_x crossref_primary_10_1007_s11425_015_5002_8 crossref_primary_10_1214_22_AAP1794 crossref_primary_10_1016_j_aml_2017_06_001 crossref_primary_10_1016_j_spl_2024_110202 crossref_primary_10_1140_epjp_i2017_11700_9 crossref_primary_10_1155_2013_564524 crossref_primary_10_3390_math11102405 crossref_primary_10_1007_s11766_023_3759_z crossref_primary_10_1016_j_spa_2020_07_017 crossref_primary_10_1007_s11425_017_9176_0 crossref_primary_10_1007_s00245_025_10291_1 crossref_primary_10_1080_03610926_2023_2203283 crossref_primary_10_1137_21M1440189 crossref_primary_10_1007_s40305_017_0181_3 crossref_primary_10_1214_17_AAP1372 crossref_primary_10_1016_j_jmaa_2019_123436 crossref_primary_10_1214_ECP_v20_3886 crossref_primary_10_1016_j_spa_2013_10_009 crossref_primary_10_1007_s11579_017_0199_7 crossref_primary_10_1155_2014_809431 crossref_primary_10_1016_j_jfranklin_2022_03_027 crossref_primary_10_1002_mma_9308 crossref_primary_10_1007_s40995_016_0067_y crossref_primary_10_1016_j_spa_2021_07_006 crossref_primary_10_1186_s13662_020_03120_y crossref_primary_10_1080_03610926_2018_1476711 crossref_primary_10_1109_TAC_2021_3123229 crossref_primary_10_1007_s00780_018_0356_8 crossref_primary_10_1080_03610926_2021_1993259 crossref_primary_10_1016_j_spa_2012_12_009 crossref_primary_10_1007_s11425_012_4534_4 crossref_primary_10_1186_s13662_017_1242_y crossref_primary_10_3390_math13071133 crossref_primary_10_1016_j_spa_2011_04_007 crossref_primary_10_1080_00207179_2020_1765022 crossref_primary_10_1080_03610926_2019_1620954 crossref_primary_10_1007_s10614_022_10263_5 crossref_primary_10_1007_s10959_020_01057_2 crossref_primary_10_1007_s10255_008_8831_1 crossref_primary_10_1080_17442508_2019_1650042 crossref_primary_10_3390_math12131947 crossref_primary_10_1007_s11425_010_4162_9 crossref_primary_10_1214_25_EJP1300 crossref_primary_10_1080_03610926_2014_917677 crossref_primary_10_1137_S0040585X97T992264 crossref_primary_10_1080_00207179_2022_2057873 crossref_primary_10_1007_s12190_025_02374_7 crossref_primary_10_1016_j_spl_2019_03_006 crossref_primary_10_1016_j_jmaa_2018_10_025 crossref_primary_10_3934_mcrf_2025020 crossref_primary_10_1007_s00013_017_1098_0 crossref_primary_10_1016_j_jmaa_2018_08_010 crossref_primary_10_1002_asjc_2663 crossref_primary_10_1016_j_automatica_2018_05_039 crossref_primary_10_3390_math8020227 crossref_primary_10_3934_naco_2025017 crossref_primary_10_1137_100814925 crossref_primary_10_1016_j_insmatheco_2021_05_006 crossref_primary_10_1016_j_jmaa_2021_125893 crossref_primary_10_1080_03610926_2022_2158343 crossref_primary_10_1016_j_spa_2017_12_004 crossref_primary_10_1016_j_spa_2015_07_008 crossref_primary_10_1142_S0219493725500273 crossref_primary_10_1186_s13662_025_03982_0 crossref_primary_10_1007_s10883_022_09593_2 crossref_primary_10_3390_math9090988 crossref_primary_10_1016_j_jmaa_2018_05_070 crossref_primary_10_1016_j_spa_2018_07_002 crossref_primary_10_1093_jjfinec_nbaa022 crossref_primary_10_1016_j_spa_2011_09_009 crossref_primary_10_5269_bspm_51618 crossref_primary_10_1007_s11425_016_0171_4 crossref_primary_10_1137_15M1032533 crossref_primary_10_1186_s13661_022_01655_5 crossref_primary_10_1016_j_spa_2015_02_002 crossref_primary_10_1016_j_jde_2021_06_029 crossref_primary_10_1016_j_spl_2020_109024 crossref_primary_10_1007_s11464_016_0504_9 crossref_primary_10_1214_13_AAP938 crossref_primary_10_1016_j_jmateco_2013_09_005 crossref_primary_10_1137_22M1534535 crossref_primary_10_1007_s10114_014_2623_8 crossref_primary_10_1007_s10255_017_0673_2 crossref_primary_10_1080_02331888_2016_1143473 crossref_primary_10_1214_24_AAP2126 crossref_primary_10_1007_s10959_020_01058_1 crossref_primary_10_1214_12_AAP885 crossref_primary_10_1007_s00013_015_0756_3 crossref_primary_10_1080_03610926_2024_2366910 crossref_primary_10_1007_s10959_024_01334_4 crossref_primary_10_1007_s10959_024_01358_w crossref_primary_10_1214_13_AOP834 crossref_primary_10_1214_12_AIHP492 crossref_primary_10_1007_s12555_019_1010_8 crossref_primary_10_1515_rose_2022_2076 crossref_primary_10_1016_j_spl_2011_01_010 crossref_primary_10_1007_s00780_012_0192_1 crossref_primary_10_1016_S0252_9602_12_60143_X crossref_primary_10_1080_07362994_2021_1991809 crossref_primary_10_1007_s40065_025_00548_6 crossref_primary_10_1007_s10114_018_7508_9 crossref_primary_10_1016_j_amc_2020_125466 crossref_primary_10_1137_23M1593681 crossref_primary_10_1080_03610926_2021_1903504 crossref_primary_10_3390_math12020279 crossref_primary_10_3390_sym16030272 crossref_primary_10_1007_s41980_020_00490_7 crossref_primary_10_1007_s11118_022_09985_w crossref_primary_10_1155_2021_5529109 crossref_primary_10_1007_s11579_020_00264_z crossref_primary_10_1080_03610926_2018_1491991 crossref_primary_10_1155_2019_1268301 crossref_primary_10_1016_j_insmatheco_2023_01_003 crossref_primary_10_1007_s10255_024_1153_0 crossref_primary_10_4213_tvp5730 crossref_primary_10_1016_j_jmaa_2023_127282 crossref_primary_10_1007_s10474_023_01350_6 crossref_primary_10_1007_s11425_010_4031_6 crossref_primary_10_1007_s10959_020_00997_z crossref_primary_10_1016_j_jmaa_2021_125540 crossref_primary_10_1080_00207179_2019_1577562 crossref_primary_10_1002_oca_2988 crossref_primary_10_1080_14697688_2020_1777321 crossref_primary_10_1016_j_orl_2016_06_004 crossref_primary_10_1007_s10255_024_1127_2 crossref_primary_10_1137_S0040585X97T992380 crossref_primary_10_1016_j_crma_2010_07_026 crossref_primary_10_1016_j_jmaa_2023_127274 crossref_primary_10_1016_j_spl_2013_01_031 crossref_primary_10_1080_03610926_2023_2195029 crossref_primary_10_1137_15M1037639 crossref_primary_10_1155_2021_5526609 crossref_primary_10_1214_11_AAP766 crossref_primary_10_1080_00036811_2017_1377831 crossref_primary_10_1007_s10473_021_0201_6 crossref_primary_10_1016_j_qref_2023_11_002 crossref_primary_10_1080_15326349_2023_2286961 crossref_primary_10_1016_j_spa_2010_06_007 crossref_primary_10_1016_j_spl_2018_07_024 crossref_primary_10_1016_j_jmaa_2021_125569 crossref_primary_10_1016_j_spa_2013_09_010 crossref_primary_10_2478_tmmp_2024_0005 crossref_primary_10_1016_j_ijar_2012_06_002 crossref_primary_10_1016_j_spl_2024_110057 crossref_primary_10_1007_s10114_012_0726_7 crossref_primary_10_1093_rfs_hht018 crossref_primary_10_1016_j_amc_2013_12_111 crossref_primary_10_1016_j_ijar_2020_12_013 crossref_primary_10_1007_s40304_015_0055_0 crossref_primary_10_1214_17_ECP53 crossref_primary_10_1007_s11401_023_0048_3 crossref_primary_10_1007_s11425_018_9541_6 crossref_primary_10_1016_j_spa_2022_08_005 crossref_primary_10_1007_s40072_025_00354_3 crossref_primary_10_1016_j_jmaa_2017_11_019 crossref_primary_10_1080_00036811_2016_1169529 crossref_primary_10_1007_s10255_021_1002_3 crossref_primary_10_1186_s13662_019_2218_x crossref_primary_10_1007_s10959_020_00998_y crossref_primary_10_1016_j_spa_2019_08_005 crossref_primary_10_1016_j_jmaa_2025_129364 crossref_primary_10_1007_s11425_016_0079_1 crossref_primary_10_1080_03610926_2023_2220449 crossref_primary_10_1016_j_chaos_2025_116671 crossref_primary_10_1080_00207179_2018_1435907 crossref_primary_10_1080_07362994_2013_828572 crossref_primary_10_1007_s11425_011_4184_y crossref_primary_10_1080_00036811_2018_1514112 crossref_primary_10_1016_j_frl_2023_104346 crossref_primary_10_1186_s13662_019_2135_z crossref_primary_10_1016_j_jde_2024_03_013 crossref_primary_10_1016_j_neucom_2025_131195 crossref_primary_10_1007_s00245_014_9242_8 crossref_primary_10_1137_20M1314823 crossref_primary_10_1080_07362994_2016_1155159 crossref_primary_10_1155_2019_7945431 crossref_primary_10_2139_ssrn_4876371 crossref_primary_10_1007_s11425_010_3156_y crossref_primary_10_1080_00207179_2022_2070548 crossref_primary_10_1007_s11401_014_0869_1 crossref_primary_10_1016_j_spl_2025_110429 crossref_primary_10_1186_s40064_016_2388_x crossref_primary_10_1016_j_spl_2009_12_005 crossref_primary_10_1080_02331888_2016_1274312 crossref_primary_10_1080_07362994_2019_1585264 crossref_primary_10_1007_s11401_018_0122_4 crossref_primary_10_1080_07362994_2019_1585265 crossref_primary_10_1016_j_amc_2010_12_059 crossref_primary_10_1016_j_sysconle_2023_105640 crossref_primary_10_1137_S0040585X97T990708 crossref_primary_10_1016_j_chaos_2020_110269 crossref_primary_10_1016_j_jmaa_2014_11_046 crossref_primary_10_1016_j_spl_2023_109848 crossref_primary_10_1155_2014_968093 crossref_primary_10_1016_j_spa_2020_09_015 crossref_primary_10_1007_s00030_024_00986_9 crossref_primary_10_1134_S1995080224600985 crossref_primary_10_1007_s11425_015_5105_2 crossref_primary_10_1080_03610926_2024_2307454 crossref_primary_10_1080_15326349_2024_2375201 crossref_primary_10_4213_tvp5497 crossref_primary_10_1007_s11009_024_10092_z crossref_primary_10_3934_puqr_2025011 crossref_primary_10_1002_mma_70087 crossref_primary_10_1016_j_jmaa_2019_123381 crossref_primary_10_1016_j_spa_2016_02_003 crossref_primary_10_4236_jmf_2020_101004 crossref_primary_10_1016_j_jmaa_2012_09_001 crossref_primary_10_3934_puqr_2025012 crossref_primary_10_4236_jmf_2020_101003 crossref_primary_10_1080_07362994_2017_1354708 crossref_primary_10_1007_s10959_020_01038_5 crossref_primary_10_1016_j_spa_2025_104700 crossref_primary_10_1515_math_2016_0023 crossref_primary_10_1016_j_spl_2023_109977 crossref_primary_10_1007_s11425_014_4816_0 crossref_primary_10_1007_s11009_023_10045_y crossref_primary_10_1186_s13660_017_1538_1 crossref_primary_10_1007_s11425_018_9556_7 crossref_primary_10_1007_s11425_015_5095_0 crossref_primary_10_1080_00207179_2021_1916077 crossref_primary_10_1080_03610926_2018_1445860 crossref_primary_10_3390_math7010045 crossref_primary_10_1007_s11401_018_0096_2 crossref_primary_10_1016_j_spa_2016_06_002 crossref_primary_10_1016_j_chaos_2020_109927 crossref_primary_10_1155_2020_1734174 crossref_primary_10_1137_19M1304131 crossref_primary_10_1214_14_AAP1054 crossref_primary_10_1007_s11401_020_0238_1 crossref_primary_10_1016_j_spl_2015_08_027 crossref_primary_10_1186_s13660_019_2064_0 crossref_primary_10_1186_s41546_019_0038_2 crossref_primary_10_1017_jpr_2024_62 crossref_primary_10_1007_s11009_023_10010_9 crossref_primary_10_1155_2013_637106 crossref_primary_10_1016_j_jmaa_2024_129028 crossref_primary_10_1080_03610926_2019_1639747 crossref_primary_10_1002_oca_2299 crossref_primary_10_1080_00036811_2021_1877686 crossref_primary_10_1080_03610926_2021_1934027 crossref_primary_10_1137_110832227 crossref_primary_10_1080_02331888_2024_2401597 crossref_primary_10_3233_JIFS_16389 crossref_primary_10_1080_00207179_2018_1480836 crossref_primary_10_1080_03610926_2020_1786585 crossref_primary_10_1080_03610926_2024_2437517 crossref_primary_10_1080_03610926_2019_1669805 crossref_primary_10_1007_s11464_013_0288_8 crossref_primary_10_1016_j_jmaa_2017_11_053 crossref_primary_10_1080_03610926_2015_1066816 crossref_primary_10_1111_mafi_12289 crossref_primary_10_1007_s40304_015_0084_8 |
| Cites_doi | 10.1090/S0273-0979-1992-00266-5 10.1016/S0167-7152(99)00102-9 10.1016/S0764-4442(97)89796-0 10.1090/conm/351/06389 10.1007/s004400100172 10.1111/1468-0262.00337 10.1016/j.crma.2003.09.017 10.1007/s004400050214 10.1142/S0252959905000154 10.1214/ECP.v5-1025 10.1016/j.crma.2004.09.015 10.1111/1467-9965.00068 10.1016/S0764-4442(01)02062-6 10.1016/0167-6911(90)90082-6 10.1007/s10255-004-0188-5 10.2977/prims/1195190727 10.1214/105051606000000169 10.1137/S0363012992232579 10.1080/17442509208833749 10.1142/S0252959904000378 10.1111/1467-9965.00022 10.1080/13504869500000007 10.1016/j.crma.2004.01.026 10.2307/1967495 10.5802/aif.1193 |
| ContentType | Journal Article |
| Copyright | 2008 Elsevier B.V. 2009 INIST-CNRS |
| Copyright_xml | – notice: 2008 Elsevier B.V. – notice: 2009 INIST-CNRS |
| DBID | 6I. AAFTH AAYXX CITATION IQODW DKI X2L |
| DOI | 10.1016/j.spa.2007.10.015 |
| DatabaseName | ScienceDirect Open Access Titles Elsevier:ScienceDirect:Open Access CrossRef Pascal-Francis RePEc IDEAS RePEc |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1879-209X |
| EndPage | 2253 |
| ExternalDocumentID | eeespapps_v_3a118_3ay_3a2008_3ai_3a12_3ap_3a2223_2253_htm 20956329 10_1016_j_spa_2007_10_015 S0304414907002128 |
| GroupedDBID | --K --M -~X .~1 0R~ 123 1B1 1OL 1RT 1~. 1~5 29Q 3R3 4.4 457 4G. 5VS 63O 6I. 7-5 71M 8P~ 9JN 9JO AAAKF AABNK AACTN AAEDT AAEDW AAFTH AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AARIN AAXUO ABAOU ABEFU ABFNM ABFRF ABJNI ABMAC ABUCO ABVKL ABXDB ABYKQ ACAZW ACDAQ ACGFO ACGFS ACRLP ADBBV ADEZE ADIYS ADMUD AEBSH AEFWE AEKER AENEX AEXQZ AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ APLSM ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CS3 DU5 E3Z EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA HAMUX HVGLF HX~ HZ~ IHE IXB J1W KOM LY1 M26 M41 MHUIS MO0 N9A NCXOZ O-L O9- OAUVE OHT OK1 OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ SDF SDG SES SEW SPC SPCBC SSB SSD SSW SSZ T5K TN5 UNMZH WH7 WUQ XFK XPP ZMT ~G- 9DU AATTM AAXKI AAYWO AAYXX ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO ADVLN AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD AFXIZ AGCQF AGRNS BNPGV IQODW SSH 0R 1 8P ADACO ADALY DKI G- HX HZ IPNFZ K M STF X X2L |
| ID | FETCH-LOGICAL-c464t-dfd8b01d9e3d73d501968adb88447198b5e651a23a0c19c672f24d794be8a78a3 |
| ISICitedReferencesCount | 429 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000261811700004&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0304-4149 |
| IngestDate | Wed Aug 18 03:10:07 EDT 2021 Mon Jul 21 09:16:02 EDT 2025 Sat Nov 29 05:28:49 EST 2025 Tue Nov 18 22:27:09 EST 2025 Fri Feb 23 02:21:57 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 12 |
| Keywords | Itô’s formula 60H10 Jensen’s inequality 60H30 g -expectation Itô’s integral BSDE Nonlinear probability theory Quadratic variation process Nonlinear expectation Brownian motion Gaussian process G -normal distribution SDE 60H05 Itô’s stochastic calculus G -convexity Heat equation Gaussian distribution Stochastic motion Stochastic process Stochastic integral Non linear equation Jensen's inequality Distribution function Convexity G-convexity Itô's stochastic calculus G-normal distribution Probability theory 50H10 G-expectation Itô's formula Itô formula Stochastic calculus Gaussian processes Non linear theory Itô's integral Expectation Application |
| Language | English |
| License | http://www.elsevier.com/open-access/userlicense/1.0 https://www.elsevier.com/tdm/userlicense/1.0 https://www.elsevier.com/open-access/userlicense/1.0 CC BY 4.0 |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c464t-dfd8b01d9e3d73d501968adb88447198b5e651a23a0c19c672f24d794be8a78a3 |
| OpenAccessLink | https://dx.doi.org/10.1016/j.spa.2007.10.015 |
| PageCount | 31 |
| ParticipantIDs | repec_primary_eeespapps_v_3a118_3ay_3a2008_3ai_3a12_3ap_3a2223_2253_htm pascalfrancis_primary_20956329 crossref_primary_10_1016_j_spa_2007_10_015 crossref_citationtrail_10_1016_j_spa_2007_10_015 elsevier_sciencedirect_doi_10_1016_j_spa_2007_10_015 |
| PublicationCentury | 2000 |
| PublicationDate | 2008-12-01 |
| PublicationDateYYYYMMDD | 2008-12-01 |
| PublicationDate_xml | – month: 12 year: 2008 text: 2008-12-01 day: 01 |
| PublicationDecade | 2000 |
| PublicationPlace | Amsterdam |
| PublicationPlace_xml | – name: Amsterdam |
| PublicationSeriesTitle | Stochastic Processes and their Applications |
| PublicationTitle | Stochastic processes and their applications |
| PublicationYear | 2008 |
| Publisher | Elsevier B.V Elsevier |
| Publisher_xml | – name: Elsevier B.V – name: Elsevier |
| References | Chung, Williams (b10) 1990 Artzner, Delbaen, Eber, Heath (b2) 1999; 9 Krylov (b30) 1980 Ph. Artzner, F. Delbaen, J.-M. Eber, D. Heath, Thinking Coherently, RISK 10, November, 1997, pp. 68–71 Peng (b38) 1999; 113 3 Jan 2006), 2006 (in press Peng (b40) 2005; 26B 24 Jan 2005), 2005 Fleming, Soner (b19) 1992 Revuz, Yor (b47) 1991 Brownian motion and dynamic risk measure under volatility uncertainty, preprint in Coquet, Hu, Mémin, Peng (b11) 2001 Protter (b46) 1990 Huber (b21) 1981 S. Peng, M. Xu, Numerical calculations to solve BSDE, 2003, preprint Yong, Zhou (b51) 1999 Jiang (b26) 2004; 338 Chen (b5) 1998; 326 Yosida (b52) 1980 Stable sets, risk measures and E.G. Rosazza, Some examples of risk measures via Denis, Martinin (b17) 2006; 16 Chen, Kulperger, Jiang (b7) 2003 Itô (b23) 1942; No. 1077 Ikeda, Watanabe (b22) 1981 Chen, Peng (b8) 1998; 34 F. Delbaen, E. Rosazza Gianin, S. Peng P. Barrieu, N. El Karoui, Pricing, hedging and optimally designing derivatives via minimization of risk measures, Contemp. Math. 2004 (in press), preprint expectations, preprint, Insurance Math. Econom. 2003 (in press) Itô, McKean (b24) 1965 Jiang, Chen (b27) 2004; 20 14 Sep 2005 Feyel, de La Pradelle (b18) 1989; 39 Peng (b39) 2004; 20 He, Wang, Yan (b20) 1992 2007 Karatzas, Shreve (b29) 1988 Delbaen (b15) 2002 Brownian motion and related stochastic calculus of Itô’s type, in: Proceedings of the 2005 Abel Symposium, preprint (pdf-file available in Nisio (b33) 1976 Chen, Peng (b9) 2000; 46 P. Cheridito, H.M. Soner, N. Touzi, N. Victoir, Second order backward stochastic differential equations and fully non-linear parabolic PDEs, preprint (pdf-file available in Øksendal (b34) 1998 S. Peng Peng (b41) 2004; 339 S. Peng, Dynamically consistent nonlinear evaluations and expectations, preprint (pdf-file available in Coquet, Hu, Memin, Peng (b12) 2002; 123 convexity and their applications, 2007, preprint Jiang, Chen (b28) 2004; 25B Lyons (b31) 1995; 2 Nisio (b32) 1976; 13 Peng (b36) 1997; vol. 364 expectations, 2005, preprint G. Jia, S. Peng, A new look at Jensen’s inequality for g expectations Peng (b35) 1992; 38 Peng (b37) 1997 Daniell (b14) 1918; 19 Briand, Coquet, Hu, Mémin, Peng (b3) 2000; 5 Chen, Epstein (b6) 2002; 70 Expectation Crandall, Ishii, Lions (b13) 1992; 27 Yan (b50) 1998 Yong (10.1016/j.spa.2007.10.015_b51) 1999 Chen (10.1016/j.spa.2007.10.015_b8) 1998; 34 Chen (10.1016/j.spa.2007.10.015_b9) 2000; 46 Dellacherie (10.1016/j.spa.2007.10.015_fr1) 1978 10.1016/j.spa.2007.10.015_b25 Jiang (10.1016/j.spa.2007.10.015_b28) 2004; 25B Chung (10.1016/j.spa.2007.10.015_b10) 1990 Denis (10.1016/j.spa.2007.10.015_b17) 2006; 16 Peng (10.1016/j.spa.2007.10.015_b41) 2004; 339 Chen (10.1016/j.spa.2007.10.015_b6) 2002; 70 Pardoux (10.1016/j.spa.2007.10.015_fr4) 1990; 14 Yosida (10.1016/j.spa.2007.10.015_b52) 1980 Chen (10.1016/j.spa.2007.10.015_b7) 2003 Peng (10.1016/j.spa.2007.10.015_b38) 1999; 113 Karatzas (10.1016/j.spa.2007.10.015_b29) 1988 El Karoui (10.1016/j.spa.2007.10.015_fr3) 1997; 7 Peng (10.1016/j.spa.2007.10.015_b36) 1997; vol. 364 Peng (10.1016/j.spa.2007.10.015_b37) 1997 Peng (10.1016/j.spa.2007.10.015_fr5) 2004; vol. 1856 Protter (10.1016/j.spa.2007.10.015_b46) 1990 Peng (10.1016/j.spa.2007.10.015_b39) 2004; 20 Itô (10.1016/j.spa.2007.10.015_b24) 1965 Krylov (10.1016/j.spa.2007.10.015_b30) 1980 Øksendal (10.1016/j.spa.2007.10.015_b34) 1998 Artzner (10.1016/j.spa.2007.10.015_b2) 1999; 9 Coquet (10.1016/j.spa.2007.10.015_b11) 2001 Peng (10.1016/j.spa.2007.10.015_b35) 1992; 38 El Karoui (10.1016/j.spa.2007.10.015_fr2) 1995; 33 Lyons (10.1016/j.spa.2007.10.015_b31) 1995; 2 Nisio (10.1016/j.spa.2007.10.015_b33) 1976 Yan (10.1016/j.spa.2007.10.015_b50) 1998 Briand (10.1016/j.spa.2007.10.015_b3) 2000; 5 Jiang (10.1016/j.spa.2007.10.015_b26) 2004; 338 10.1016/j.spa.2007.10.015_fr7 Delbaen (10.1016/j.spa.2007.10.015_b15) 2002 10.1016/j.spa.2007.10.015_b49 10.1016/j.spa.2007.10.015_fr6 Chen (10.1016/j.spa.2007.10.015_b5) 1998; 326 10.1016/j.spa.2007.10.015_b45 10.1016/j.spa.2007.10.015_b48 10.1016/j.spa.2007.10.015_b42 10.1016/j.spa.2007.10.015_b43 10.1016/j.spa.2007.10.015_b44 Coquet (10.1016/j.spa.2007.10.015_b12) 2002; 123 Crandall (10.1016/j.spa.2007.10.015_b13) 1992; 27 10.1016/j.spa.2007.10.015_b4 Itô (10.1016/j.spa.2007.10.015_b23) 1942; No. 1077 Peng (10.1016/j.spa.2007.10.015_b40) 2005; 26B 10.1016/j.spa.2007.10.015_b1 Revuz (10.1016/j.spa.2007.10.015_b47) 1991 10.1016/j.spa.2007.10.015_b16 Huber (10.1016/j.spa.2007.10.015_b21) 1981 Feyel (10.1016/j.spa.2007.10.015_b18) 1989; 39 He (10.1016/j.spa.2007.10.015_b20) 1992 Daniell (10.1016/j.spa.2007.10.015_b14) 1918; 19 Fleming (10.1016/j.spa.2007.10.015_b19) 1992 Nisio (10.1016/j.spa.2007.10.015_b32) 1976; 13 Ikeda (10.1016/j.spa.2007.10.015_b22) 1981 Jiang (10.1016/j.spa.2007.10.015_b27) 2004; 20 |
| References_xml | – year: 1990 ident: b10 article-title: Introduction to Stochastic Integration – reference: -convexity and their applications, 2007, preprint – year: 1981 ident: b21 article-title: Robust Statistics – reference: , 2007 – reference: 24 Jan 2005), 2005 – reference: S. Peng, M. Xu, Numerical calculations to solve BSDE, 2003, preprint – reference: -Expectation, – year: 1990 ident: b46 article-title: Stochastic Integration and Differential Equations – reference: F. Delbaen, E. Rosazza Gianin, S. Peng, – reference: -expectations, preprint, Insurance Math. Econom. 2003 (in press) – volume: 27 start-page: 1 year: 1992 end-page: 67 ident: b13 article-title: User’S guide to viscosity solutions of second order partial differential equations publication-title: Bull. Amer. Math. Soc. – volume: 19 start-page: 279 year: 1918 end-page: 294 ident: b14 article-title: A general form of integral publication-title: Ann. Math. – reference: P. Cheridito, H.M. Soner, N. Touzi, N. Victoir, Second order backward stochastic differential equations and fully non-linear parabolic PDEs, preprint (pdf-file available in – start-page: 297 year: 1976 end-page: 325 ident: b33 article-title: On stochastic optimal controls and envelope of Markovian semi-groups publication-title: Proc. of int. Symp. Kyoto – volume: 34 start-page: 197 year: 1998 end-page: 208 ident: b8 article-title: A nonlinear Doob–Meyer type decomposition and its application publication-title: SUT J. Math. (Japan) – volume: 5 year: 2000 ident: b3 article-title: A converse comparison theorem for BSDEs and related properties of publication-title: Electron. Comm. Probab. – reference: Ph. Artzner, F. Delbaen, J.-M. Eber, D. Heath, Thinking Coherently, RISK 10, November, 1997, pp. 68–71 – reference: P. Barrieu, N. El Karoui, Pricing, hedging and optimally designing derivatives via minimization of risk measures, Contemp. Math. 2004 (in press), preprint – year: 1997 ident: b37 article-title: BSDE and stochastic optimizations publication-title: Topics in Stochastic Analysis – volume: 20 start-page: 1 year: 2004 end-page: 24 ident: b39 article-title: Filtration consistent nonlinear expectations and evaluations of contingent claims publication-title: Acta Math. Appl. Sinica (English Ser.) – reference: -Brownian motion and dynamic risk measure under volatility uncertainty, preprint in – year: 1988 ident: b29 article-title: Brownian Motion and Stochastic Calculus – volume: 326 start-page: 483 year: 1998 end-page: 488 ident: b5 article-title: A property of backward stochastic differential equations publication-title: C.R. Acad. Sci. Paris Sér. I – reference: -Stable sets, risk measures and – reference: S. Peng, Dynamically consistent nonlinear evaluations and expectations, preprint (pdf-file available in – start-page: 577 year: 2001 end-page: 581 ident: b11 article-title: A general converse comparison theorem for backward stochastic differential equations publication-title: C.R. Acad. Sci. Paris, t.333, Serie I – volume: 39 start-page: 875 year: 1989 end-page: 908 ident: b18 article-title: Espaces de Sobolev gaussiens publication-title: Ann. Inst. Fourier – reference: , 14 Sep 2005) – volume: 338 start-page: 575 year: 2004 end-page: 580 ident: b26 article-title: Some results on the uniqueness of generators of backward stochastic differential equations publication-title: C. R. Acad. Sci. Paris, Ser. I – volume: vol. 364 start-page: 141 year: 1997 end-page: 159 ident: b36 article-title: Backward SDE and related publication-title: Backward Stochastic Differential Equations – year: 1980 ident: b30 article-title: Controlled Diffusion Processes – volume: 46 start-page: 169 year: 2000 end-page: 175 ident: b9 article-title: A general downcrossing inequality for publication-title: Statist. Probab. Lett. – reference: S. Peng, – year: 1981 ident: b22 article-title: Stochastic Differential Equations and Diffusion Processes – volume: 38 start-page: 119 year: 1992 end-page: 134 ident: b35 article-title: A generalized dynamic programming principle and Hamilton–Jacobi–Bellman equation publication-title: Stochast. Stochast. Rep. – volume: 113 start-page: 473 year: 1999 end-page: 499 ident: b38 article-title: Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob–Meyer’s type publication-title: Prob. Theory Related Fields – year: 1991 ident: b47 article-title: Continuous Martingales and Brownian Motion – year: 2002 ident: b15 article-title: Coherent Risk Measures (Lectures given at the Cattedra Galileiana at the Scuola Normale di Pisa, March 2000) – volume: 16 start-page: 827 year: 2006 end-page: 852 ident: b17 article-title: A theoretical framework for the pricing of contingent claims in the presence of model uncertainty publication-title: Ann. Appl. Probab. – volume: 2 start-page: 117 year: 1995 end-page: 133 ident: b31 article-title: Uncertain volatility and the risk free synthesis of derivatives publication-title: Appl. Math. Finance – year: 1980 ident: b52 article-title: Functional Analysis – volume: 20 start-page: 507 year: 2004 end-page: 512 ident: b27 article-title: A result on the probability measures dominated by publication-title: Acta Math. Appl. Sinica (English Ser.) – reference: -Brownian motion and related stochastic calculus of Itô’s type, in: Proceedings of the 2005 Abel Symposium, preprint (pdf-file available in: – volume: 13 start-page: 513 year: 1976 end-page: 537 ident: b32 article-title: On a nonlinear semigroup attached to optimal stochastic control publication-title: Publ. RIMS, Kyoto Univ. – reference: , 3 Jan 2006), 2006 (in press) – start-page: 725 year: 2003 end-page: 730 ident: b7 article-title: Jensen’s inequality for publication-title: C. R. Acad. Sci. Paris Sér. I 337 – reference: -expectations, 2005, preprint – volume: 339 start-page: 585 year: 2004 end-page: 589 ident: b41 article-title: Dynamical evaluations publication-title: C. R. Acad. Sci. Paris, Ser. I – year: 1998 ident: b50 article-title: Lecture Note on Measure Theory – volume: 25B start-page: 401 year: 2004 end-page: 412 ident: b28 article-title: On Jensen’s inequality for publication-title: Chin. Ann. Math. – year: 1999 ident: b51 article-title: Stochastic Controls: Hamiltonian Systems and HJB Equations – reference: E.G. Rosazza, Some examples of risk measures via – year: 1998 ident: b34 article-title: Stochastic Differential Equations – reference: G. Jia, S. Peng, A new look at Jensen’s inequality for g expectations: – volume: 9 start-page: 203 year: 1999 end-page: 228 ident: b2 article-title: Coherent measures of risk publication-title: Math. Finance – volume: 26B start-page: 159 year: 2005 end-page: 184 ident: b40 article-title: Nonlinear expectations and nonlinear Markov chains publication-title: Chin. Ann. Math. – volume: 70 start-page: 1403 year: 2002 end-page: 1443 ident: b6 article-title: Ambiguity, risk and asset returns in continuous time publication-title: Econometrica – year: 1992 ident: b19 article-title: Controlled Markov Processes and Viscosity Solutions – year: 1965 ident: b24 article-title: Diffusion Processes and Their Sample Paths – volume: No. 1077 year: 1942 ident: b23 article-title: Differential equations determining a Markoff process publication-title: J. Pan-Japan Math. Coll. – year: 1992 ident: b20 article-title: Semimartingale Theory and Stochastic Calculus – volume: 123 start-page: 1 year: 2002 end-page: 27 ident: b12 article-title: Filtration-consistent nonlinear expectations and related publication-title: Probab. Theory Related Fields – volume: 27 start-page: 1 issue: 1 year: 1992 ident: 10.1016/j.spa.2007.10.015_b13 article-title: User’S guide to viscosity solutions of second order partial differential equations publication-title: Bull. Amer. Math. Soc. doi: 10.1090/S0273-0979-1992-00266-5 – year: 1992 ident: 10.1016/j.spa.2007.10.015_b20 – volume: 46 start-page: 169 issue: 2 year: 2000 ident: 10.1016/j.spa.2007.10.015_b9 article-title: A general downcrossing inequality for g-martingales publication-title: Statist. Probab. Lett. doi: 10.1016/S0167-7152(99)00102-9 – volume: 326 start-page: 483 issue: 4 year: 1998 ident: 10.1016/j.spa.2007.10.015_b5 article-title: A property of backward stochastic differential equations publication-title: C.R. Acad. Sci. Paris Sér. I doi: 10.1016/S0764-4442(97)89796-0 – ident: 10.1016/j.spa.2007.10.015_b4 doi: 10.1090/conm/351/06389 – volume: 123 start-page: 1 year: 2002 ident: 10.1016/j.spa.2007.10.015_b12 article-title: Filtration-consistent nonlinear expectations and related g-expectations publication-title: Probab. Theory Related Fields doi: 10.1007/s004400100172 – ident: 10.1016/j.spa.2007.10.015_b43 – volume: 70 start-page: 1403 issue: 4 year: 2002 ident: 10.1016/j.spa.2007.10.015_b6 article-title: Ambiguity, risk and asset returns in continuous time publication-title: Econometrica doi: 10.1111/1468-0262.00337 – start-page: 725 year: 2003 ident: 10.1016/j.spa.2007.10.015_b7 article-title: Jensen’s inequality for g-expectation: Part 1 publication-title: C. R. Acad. Sci. Paris Sér. I 337 doi: 10.1016/j.crma.2003.09.017 – year: 1988 ident: 10.1016/j.spa.2007.10.015_b29 – volume: 113 start-page: 473 issue: 4 year: 1999 ident: 10.1016/j.spa.2007.10.015_b38 article-title: Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob–Meyer’s type publication-title: Prob. Theory Related Fields doi: 10.1007/s004400050214 – ident: 10.1016/j.spa.2007.10.015_fr7 – year: 1980 ident: 10.1016/j.spa.2007.10.015_b30 – year: 1965 ident: 10.1016/j.spa.2007.10.015_b24 – volume: 26B start-page: 159 issue: 2 year: 2005 ident: 10.1016/j.spa.2007.10.015_b40 article-title: Nonlinear expectations and nonlinear Markov chains publication-title: Chin. Ann. Math. doi: 10.1142/S0252959905000154 – volume: 5 year: 2000 ident: 10.1016/j.spa.2007.10.015_b3 article-title: A converse comparison theorem for BSDEs and related properties of g-expectations publication-title: Electron. Comm. Probab. doi: 10.1214/ECP.v5-1025 – year: 1998 ident: 10.1016/j.spa.2007.10.015_b34 – volume: 339 start-page: 585 year: 2004 ident: 10.1016/j.spa.2007.10.015_b41 article-title: Dynamical evaluations publication-title: C. R. Acad. Sci. Paris, Ser. I doi: 10.1016/j.crma.2004.09.015 – volume: No. 1077 year: 1942 ident: 10.1016/j.spa.2007.10.015_b23 article-title: Differential equations determining a Markoff process publication-title: J. Pan-Japan Math. Coll. – year: 1978 ident: 10.1016/j.spa.2007.10.015_fr1 – volume: 9 start-page: 203 year: 1999 ident: 10.1016/j.spa.2007.10.015_b2 article-title: Coherent measures of risk publication-title: Math. Finance doi: 10.1111/1467-9965.00068 – year: 1990 ident: 10.1016/j.spa.2007.10.015_b46 – ident: 10.1016/j.spa.2007.10.015_b44 – ident: 10.1016/j.spa.2007.10.015_b48 – start-page: 577 year: 2001 ident: 10.1016/j.spa.2007.10.015_b11 article-title: A general converse comparison theorem for backward stochastic differential equations publication-title: C.R. Acad. Sci. Paris, t.333, Serie I doi: 10.1016/S0764-4442(01)02062-6 – year: 1991 ident: 10.1016/j.spa.2007.10.015_b47 – year: 1998 ident: 10.1016/j.spa.2007.10.015_b50 – volume: 14 start-page: 55 issue: 1 year: 1990 ident: 10.1016/j.spa.2007.10.015_fr4 article-title: Adapted solution of a backward stochastic differential equation publication-title: Syst. Control Lett. doi: 10.1016/0167-6911(90)90082-6 – volume: 20 start-page: 1 issue: 2 year: 2004 ident: 10.1016/j.spa.2007.10.015_b39 article-title: Filtration consistent nonlinear expectations and evaluations of contingent claims publication-title: Acta Math. Appl. Sinica (English Ser.) – year: 1997 ident: 10.1016/j.spa.2007.10.015_b37 article-title: BSDE and stochastic optimizations – year: 1981 ident: 10.1016/j.spa.2007.10.015_b21 – volume: 20 start-page: 507 issue: 3 year: 2004 ident: 10.1016/j.spa.2007.10.015_b27 article-title: A result on the probability measures dominated by g-expectation publication-title: Acta Math. Appl. Sinica (English Ser.) doi: 10.1007/s10255-004-0188-5 – volume: 13 start-page: 513 year: 1976 ident: 10.1016/j.spa.2007.10.015_b32 article-title: On a nonlinear semigroup attached to optimal stochastic control publication-title: Publ. RIMS, Kyoto Univ. doi: 10.2977/prims/1195190727 – volume: 16 start-page: 827 issue: 2 year: 2006 ident: 10.1016/j.spa.2007.10.015_b17 article-title: A theoretical framework for the pricing of contingent claims in the presence of model uncertainty publication-title: Ann. Appl. Probab. doi: 10.1214/105051606000000169 – start-page: 297 year: 1976 ident: 10.1016/j.spa.2007.10.015_b33 article-title: On stochastic optimal controls and envelope of Markovian semi-groups – year: 1980 ident: 10.1016/j.spa.2007.10.015_b52 – year: 1999 ident: 10.1016/j.spa.2007.10.015_b51 – volume: 33 issue: 1 year: 1995 ident: 10.1016/j.spa.2007.10.015_fr2 article-title: Dynamic programming and pricing of contingent claims in incomplete market publication-title: SIAM J. Control Optim. doi: 10.1137/S0363012992232579 – volume: 38 start-page: 119 issue: 2 year: 1992 ident: 10.1016/j.spa.2007.10.015_b35 article-title: A generalized dynamic programming principle and Hamilton–Jacobi–Bellman equation publication-title: Stochast. Stochast. Rep. doi: 10.1080/17442509208833749 – ident: 10.1016/j.spa.2007.10.015_b49 – ident: 10.1016/j.spa.2007.10.015_b45 – volume: 25B start-page: 401 issue: 3 year: 2004 ident: 10.1016/j.spa.2007.10.015_b28 article-title: On Jensen’s inequality for g-expectation publication-title: Chin. Ann. Math. doi: 10.1142/S0252959904000378 – ident: 10.1016/j.spa.2007.10.015_b1 – ident: 10.1016/j.spa.2007.10.015_b16 – volume: 7 start-page: 1 issue: 1 year: 1997 ident: 10.1016/j.spa.2007.10.015_fr3 article-title: Backward stochastic differential equation in finance publication-title: Math. Finance doi: 10.1111/1467-9965.00022 – year: 2002 ident: 10.1016/j.spa.2007.10.015_b15 – year: 1981 ident: 10.1016/j.spa.2007.10.015_b22 – volume: 2 start-page: 117 year: 1995 ident: 10.1016/j.spa.2007.10.015_b31 article-title: Uncertain volatility and the risk free synthesis of derivatives publication-title: Appl. Math. Finance doi: 10.1080/13504869500000007 – volume: vol. 1856 start-page: 143 year: 2004 ident: 10.1016/j.spa.2007.10.015_fr5 article-title: Nonlinear expectation, nonlinear evaluations and risk measures – volume: 338 start-page: 575 year: 2004 ident: 10.1016/j.spa.2007.10.015_b26 article-title: Some results on the uniqueness of generators of backward stochastic differential equations publication-title: C. R. Acad. Sci. Paris, Ser. I doi: 10.1016/j.crma.2004.01.026 – volume: 34 start-page: 197 issue: 2 year: 1998 ident: 10.1016/j.spa.2007.10.015_b8 article-title: A nonlinear Doob–Meyer type decomposition and its application publication-title: SUT J. Math. (Japan) – ident: 10.1016/j.spa.2007.10.015_b42 – volume: vol. 364 start-page: 141 year: 1997 ident: 10.1016/j.spa.2007.10.015_b36 article-title: Backward SDE and related g-expectation – year: 1990 ident: 10.1016/j.spa.2007.10.015_b10 – ident: 10.1016/j.spa.2007.10.015_b25 – volume: 19 start-page: 279 year: 1918 ident: 10.1016/j.spa.2007.10.015_b14 article-title: A general form of integral publication-title: Ann. Math. doi: 10.2307/1967495 – volume: 39 start-page: 875 year: 1989 ident: 10.1016/j.spa.2007.10.015_b18 article-title: Espaces de Sobolev gaussiens publication-title: Ann. Inst. Fourier doi: 10.5802/aif.1193 – year: 1992 ident: 10.1016/j.spa.2007.10.015_b19 – ident: 10.1016/j.spa.2007.10.015_fr6 |
| SSID | ssj0001221 |
| Score | 2.425703 |
| Snippet | We develop a notion of nonlinear expectation–
G
-expectation–generated by a nonlinear heat equation with infinitesimal generator
G
. We first study... We develop a notion of nonlinear expectation-G-expectation-generated by a nonlinear heat equation with infinitesimal generator G. We first study... |
| SourceID | repec pascalfrancis crossref elsevier |
| SourceType | Index Database Enrichment Source Publisher |
| StartPage | 2223 |
| SubjectTerms | [formula omitted]-convexity [formula omitted]-expectation [formula omitted]-normal distribution Brownian motion BSDE Distribution theory Exact sciences and technology g-expectation G-expectation G-normal distribution BSDE SDE Nonlinear probability theory Nonlinear expectation Brownian motion Ito's stochastic calculus Ito's integral Ito's formula Gaussian process Quadratic variation process Jensen's inequality G-convexity Gaussian process Itô’s formula Itô’s integral Itô’s stochastic calculus Jensen’s inequality Mathematics Nonlinear expectation Nonlinear probability theory Probability and statistics Probability theory and stochastic processes Probability theory on algebraic and topological structures Quadratic variation process Sciences and techniques of general use SDE Stochastic analysis Stochastic processes |
| Title | Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation |
| URI | https://dx.doi.org/10.1016/j.spa.2007.10.015 http://econpapers.repec.org/article/eeespapps/v_3a118_3ay_3a2008_3ai_3a12_3ap_3a2223-2253.htm |
| Volume | 118 |
| WOSCitedRecordID | wos000261811700004&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1879-209X dateEnd: 20180131 omitProxy: false ssIdentifier: ssj0001221 issn: 0304-4149 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1bb9MwFLZKxwMTQly1cpnywBNVUGO7sfNYoTFAYprEEH2LHNtRO20harpq_Dd-HOfEzmVlTIDgoVbl1nbr78vxsX0uhLykNIp1onUI6rEJecx4mAmWhLmhIouNtSLXdbIJcXQk5_PkeDD43vjCbM5EUcjLy6T8r1BDHYCNrrN_AHfbKVTAewAdSoAdyt8CvnapDQ1G7XcRN8aHYb3ZxkfZJe1xRuVoBgfqJmh_eqEwXPMY8MLTwKpOjruCdhj_X_cu670W-6lrUjpHA1s1ppjL1bh_Kd6JXn8uvVh66yOcDFv1-zq-pq_Zdl_NCYXcsvZoXGd6ko1NeMgjF6v0tXWSV4oEcKzz6naiuZPNF629tZe01Pkp-1UbxBK7dkVwhxOn2MoFrERbPudBuhVo21pbYXK1Kt2kTMHQUH6DV52ok6klVlIoSqyD0VMcM12sz2-RHSqmiRySndn7g_mHVhOIaO331_7d5la9ti_c-kG_0ovulqoC9HOXZgW2UCsLyPd0oJP75J7fvAQzR7oHZGCLh2T3Yxv5t3pEvvxEv6CjX-DoFwC8gadf0NEvaOgX1PQLrtDvMfn89uDkzbvQJ-8INY_5OjS5kdkkMollRjAzxThMUplMSg76UCKzqY2nkaJMTXSU6FjQnHIDq0NmpRJSsSdkWHwt7B4JGPaDiYhyqnlmlNQ2yiIuJKcKtP_JiEyaqUu1j2yPCVbO0saE8TSF2caMqwKrYLZH5FXbpHRhXW76Mm_wSL1e6vTNFEh2U7P9K9i1A1EM_sloMiKHNZjtB3_NwKf_rKdn5E73CD8nw_Xqwr4gt_VmvaxW-57gPwB1Jd_c |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Multi-dimensional+G-Brownian+motion+and+related+stochastic+calculus+under+G-expectation&rft.jtitle=Stochastic+processes+and+their+applications&rft.au=Peng%2C+Shige&rft.series=Stochastic+Processes+and+their+Applications&rft.date=2008-12-01&rft.pub=Elsevier&rft.issn=0304-4149&rft.eissn=1879-209X&rft.volume=118&rft.issue=12&rft.spage=2223&rft.epage=2253&rft_id=info:doi/10.1016%2Fj.spa.2007.10.015&rft.externalDocID=eeespapps_v_3a118_3ay_3a2008_3ai_3a12_3ap_3a2223_2253_htm |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0304-4149&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0304-4149&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0304-4149&client=summon |