Uniform-in-time estimates for mean-field type SDEs and applications
Via constructing an asymptotic coupling by reflection, in this paper we establish uniform-in-time estimates on probability distributions for mean-field type SDEs, where the drift terms under consideration are dissipative merely in the long distance. As applications, we (i) explore the long time esti...
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| Published in: | Journal of Differential Equations Vol. 440; p. 113445 |
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| Language: | English |
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| ISSN: | 0022-0396 |
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| Abstract | Via constructing an asymptotic coupling by reflection, in this paper we establish uniform-in-time estimates on probability distributions for mean-field type SDEs, where the drift terms under consideration are dissipative merely in the long distance. As applications, we (i) explore the long time estimate on probability distributions associated with an SDE and its delay version; (ii) investigate the issue on uniform-in-time propagation of chaos for McKean-Vlasov SDEs, where the drifts might be singular with respect to the spatial variables; (iii) tackle the discretization error bounds in an infinite-time horizon for stochastic algorithms (e.g. backward/tamed/adaptive Euler-Maruyama schemes as three typical candidates) associated with McKean-Vlasov SDEs. |
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| AbstractList | Via constructing an asymptotic coupling by reflection, in this paper we establish uniform-in-time estimates on probability distributions for mean-field type SDEs, where the drift terms under consideration are dissipative merely in the long distance. As applications, we (i) explore the long time estimate on probability distributions associated with an SDE and its delay version; (ii) investigate the issue on uniform-in-time propagation of chaos for McKean-Vlasov SDEs, where the drifts might be singular with respect to the spatial variables; (iii) tackle the discretization error bounds in an infinite-time horizon for stochastic algorithms (e.g. backward/tamed/adaptive Euler-Maruyama schemes as three typical candidates) associated with McKean-Vlasov SDEs. |
| ArticleNumber | 113445 |
| Author | Bao, Jianhai Hao, Jiaqing |
| Author_xml | – sequence: 1 givenname: Jianhai surname: Bao fullname: Bao, Jianhai email: jianhaibao@tju.edu.cn – sequence: 2 givenname: Jiaqing surname: Hao fullname: Hao, Jiaqing email: hjq_0227@tju.edu.cn |
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| Cites_doi | 10.1016/j.jde.2018.04.052 10.1007/s00440-014-0583-7 10.1214/22-AIHP1337 10.1016/j.spa.2018.10.002 10.1016/j.spa.2006.03.002 10.1093/imanum/draa099 10.1016/j.jfa.2005.12.010 10.1214/11-AAP803 10.1007/s00440-015-0673-1 10.1137/S0036142901389530 10.1016/j.spa.2015.04.001 10.1016/j.cam.2021.113725 10.1090/proc/14612 10.1007/s10959-021-01082-9 10.1214/21-AAP1760 10.1016/j.spa.2017.05.006 10.1081/SAP-200026423 10.1214/19-AAP1507 10.5802/jep.235 10.1093/imanum/drad038 10.1016/S0304-4149(02)00150-3 10.1214/15-AAP1140 10.1016/j.na.2015.01.012 10.4171/jems/1413 10.1287/moor.2022.0307 |
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| SubjectTerms | Asymptotic coupling by reflection Mean-field type SDE Propagation of chaos Stochastic algorithm Uniform-in-time estimate |
| Title | Uniform-in-time estimates for mean-field type SDEs and applications |
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