Infinite dimensional weak Dirichlet processes and convolution type processes
The present paper continues the study of infinite dimensional calculus via regularization, started by C. Di Girolami and the second named author, introducing the notion of weak Dirichlet process in this context. Such a process X, taking values in a Banach space H, is the sum of a local martingale an...
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| Veröffentlicht in: | Stochastic processes and their applications Jg. 127; H. 1; S. 325 - 357 |
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| Abstract | The present paper continues the study of infinite dimensional calculus via regularization, started by C. Di Girolami and the second named author, introducing the notion of weak Dirichlet process in this context. Such a process X, taking values in a Banach space H, is the sum of a local martingale and a suitable orthogonal process.
The concept of weak Dirichlet process fits the notion of convolution type processes, a class including mild solutions for stochastic evolution equations on infinite dimensional Hilbert spaces and in particular of several classes of stochastic partial differential equations (SPDEs).
In particular the mentioned decomposition appears to be a substitute of an Itô’s type formula applied to f(t,X(t)) where f:[0,T]×H→R is a C0,1 function and X a convolution type process. |
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| AbstractList | The present paper continues the study of infinite dimensional calculus via regularization, started by C. Di Girolami and the second named author, introducing the notion of weak Dirichlet process in this context. Such a process X, taking values in a Banach space H, is the sum of a local martingale and a suitable orthogonal process.
The concept of weak Dirichlet process fits the notion of convolution type processes, a class including mild solutions for stochastic evolution equations on infinite dimensional Hilbert spaces and in particular of several classes of stochastic partial differential equations (SPDEs).
In particular the mentioned decomposition appears to be a substitute of an Itô’s type formula applied to f(t,X(t)) where f:[0,T]×H→R is a C0,1 function and X a convolution type process. The present paper continues the study of infinite dimensional calculus via regularization, started by C. Di Girolami and the second named author, introducing the notion of weak Dirichlet process in this context. Such a process X, taking values in a Banach space H, is the sum of a local martingale and a suitable orthogonal process. The concept of weak Dirichlet process fits the notion of convolution type processes, a class including mild solutions for stochastic evolution equations on infinite dimensional Hilbert spaces and in particular of several classes of stochastic partial differential equations (SPDEs). In particular the mentioned decomposition appears to be a substitute of an Itô's type formula applied to f (t, X(t)) where f : [0, T ] × H → R is a C 0,1 function and X a convolution type processes. |
| Author | Fabbri, Giorgio Russo, Francesco |
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| Cites_doi | 10.1137/100788574 10.1214/009117906000001006 10.1016/j.jfa.2008.03.015 10.1016/j.crma.2010.11.032 10.1142/S0219025712500075 10.1016/j.spa.2006.04.008 10.1142/S0219025715500058 10.1007/BF01195073 10.4153/CJM-1990-046-8 10.1016/j.spa.2006.04.009 10.1016/S0304-4149(02)00238-7 10.1007/s00245-004-0814-x 10.1007/s11118-006-9013-5 |
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| Keywords | Generalized Fukushima decomposition Convolution type processes 35R60 Stochastic partial differential equations Calculus via regularization 60H30 Covariation and quadratic variation Tensor analysis Infinite dimensional analysis Dirichlet processes 60H05 60H15 Covariation and Quadratic variation |
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| References | Di Girolami, Russo (br000045) 2011; 349 Pazy (br000155) 1983; vol. 44 Coquet, Jakubowski, Mémin, Słomiński (br000015) 2006; vol. 1874 Ma, Röckner (br000130) 1992 Dunford, Schwartz (br000070) 1988 Dinculeanu (br000065) 2000 Di Girolami, Russo (br000055) 2014; 51 Gubinelli, Lejay, Tindel (br000110) 2006; 25 Ryan (br000190) 2002 Métivier (br000135) 1982 Russo, Vallois (br000170) 1991; 312 Brzezniak, Serrano (br000010) 2013; 51 Leon (br000125) 1990; 42 Gozzi, Russo (br000105) 2006; 116 Fuhrman, Tessitore (br000090) 2005; 51 Pronk, Veraar (br000165) 2015; 18 Diestel, Uhl (br000060) 1977 Gawarecki, Mandrekar (br000095) 2011 Ondreját (br000150) 2004; 426 Métivier, Pellaumail (br000140) 1980 Russo, Vallois (br000180) 1993; vol. 8 Stein (br000195) 1970 Da Prato, Zabczyk (br000025) 1992 Föllmer (br000085) 1981; vol. 851 G. Da Prato, A. Jentzen, M. Röckner, A mild Itô formula for SPDEs, 2011. Preprint Arxiv Di Girolami, Russo (br000050) 2012; 15 Bensoussan, Da Prato, Delfour, Mitter (br000005) 2007 Da Prato, Zabczyk (br000030) 1996 Krylov, Rozovskii (br000120) 2007; vol. 2 Meyer (br000145) 1977; vol. 581 Errami, Russo (br000075) 2003; 104 Russo, Vallois (br000175) 1993; 97 Denis (br000035) 2004; 10 . C. Di Girolami, F. Russo, Infinite dimensional stochastic calculus via regularization, 2010. Preprint HAL-INRIA van Neerven, Veraar, Weis (br000200) 2007; 35 Russo, Vallois (br000185) 2007; vol. 1899 G. Fabbri, F. Russo, Infinite dimensional weak Dirichlet processes, stochastic PDEs and optimal control (unpublished), 2012. Preprint Karatzas, Shreve (br000115) 1988 Peszat, Zabczyk (br000160) 2007 Van Neerven, Veraar, Weis (br000205) 2008; 255 Gozzi, Russo (br000100) 2006; 116 Di Girolami (10.1016/j.spa.2016.06.010_br000055) 2014; 51 Ma (10.1016/j.spa.2016.06.010_br000130) 1992 Métivier (10.1016/j.spa.2016.06.010_br000140) 1980 Ryan (10.1016/j.spa.2016.06.010_br000190) 2002 Föllmer (10.1016/j.spa.2016.06.010_br000085) 1981; vol. 851 10.1016/j.spa.2016.06.010_br000080 Pazy (10.1016/j.spa.2016.06.010_br000155) 1983; vol. 44 Errami (10.1016/j.spa.2016.06.010_br000075) 2003; 104 Métivier (10.1016/j.spa.2016.06.010_br000135) 1982 Ondreját (10.1016/j.spa.2016.06.010_br000150) 2004; 426 Peszat (10.1016/j.spa.2016.06.010_br000160) 2007 Russo (10.1016/j.spa.2016.06.010_br000185) 2007; vol. 1899 Russo (10.1016/j.spa.2016.06.010_br000180) 1993; vol. 8 Coquet (10.1016/j.spa.2016.06.010_br000015) 2006; vol. 1874 Da Prato (10.1016/j.spa.2016.06.010_br000030) 1996 Meyer (10.1016/j.spa.2016.06.010_br000145) 1977; vol. 581 Gawarecki (10.1016/j.spa.2016.06.010_br000095) 2011 van Neerven (10.1016/j.spa.2016.06.010_br000200) 2007; 35 Dunford (10.1016/j.spa.2016.06.010_br000070) 1988 Di Girolami (10.1016/j.spa.2016.06.010_br000045) 2011; 349 Russo (10.1016/j.spa.2016.06.010_br000170) 1991; 312 Gozzi (10.1016/j.spa.2016.06.010_br000100) 2006; 116 Da Prato (10.1016/j.spa.2016.06.010_br000025) 1992 Denis (10.1016/j.spa.2016.06.010_br000035) 2004; 10 Diestel (10.1016/j.spa.2016.06.010_br000060) 1977 Gubinelli (10.1016/j.spa.2016.06.010_br000110) 2006; 25 Di Girolami (10.1016/j.spa.2016.06.010_br000050) 2012; 15 Van Neerven (10.1016/j.spa.2016.06.010_br000205) 2008; 255 Bensoussan (10.1016/j.spa.2016.06.010_br000005) 2007 Dinculeanu (10.1016/j.spa.2016.06.010_br000065) 2000 Russo (10.1016/j.spa.2016.06.010_br000175) 1993; 97 Pronk (10.1016/j.spa.2016.06.010_br000165) 2015; 18 Stein (10.1016/j.spa.2016.06.010_br000195) 1970 Leon (10.1016/j.spa.2016.06.010_br000125) 1990; 42 Brzezniak (10.1016/j.spa.2016.06.010_br000010) 2013; 51 Fuhrman (10.1016/j.spa.2016.06.010_br000090) 2005; 51 10.1016/j.spa.2016.06.010_br000040 Karatzas (10.1016/j.spa.2016.06.010_br000115) 1988 10.1016/j.spa.2016.06.010_br000020 Gozzi (10.1016/j.spa.2016.06.010_br000105) 2006; 116 Krylov (10.1016/j.spa.2016.06.010_br000120) 2007; vol. 2 |
| References_xml | – year: 1992 ident: br000025 article-title: Stochastic Equations in Infinite Dimensions – volume: vol. 1899 start-page: 147 year: 2007 end-page: 185 ident: br000185 article-title: Elements of stochastic calculus via regularization publication-title: Séminaire de Probabilités XL – volume: 312 start-page: 615 year: 1991 end-page: 618 ident: br000170 article-title: Intégrales progressive, rétrograde et symétrique de processus non adaptés publication-title: C. R. Acad. Sci. Paris I – volume: 51 start-page: 2664 year: 2013 end-page: 2703 ident: br000010 article-title: Optimal relaxed control of dissipative stochastic partial differential equations in Banach spaces publication-title: SIAM J. Control Optim. – volume: 104 start-page: 259 year: 2003 end-page: 299 ident: br000075 article-title: -covariation, generalized Dirichlet processes and calculus with respect to finite cubic variation processes publication-title: Stochastic Process. Appl. – year: 2002 ident: br000190 article-title: Introduction to Tensor Products of Banach Spaces – volume: 255 start-page: 940 year: 2008 end-page: 993 ident: br000205 article-title: Stochastic evolution equations in umd Banach spaces publication-title: J. Appl. Funct. Anal. – volume: 116 start-page: 1530 year: 2006 end-page: 1562 ident: br000100 article-title: Verification theorems for stochastic optimal control problems via a time dependent Fukushima-Dirichlet decomposition publication-title: Stochastic Process. Appl. – volume: 426 start-page: 63 year: 2004 ident: br000150 article-title: Uniqueness for stochastic evolution equations in Banach spaces publication-title: Dissertationes Math. (Rozprawy Mat.) – volume: 18 start-page: 1550005 year: 2015 ident: br000165 article-title: Forward integration, convergence and non-adapted pointwise multipliers publication-title: Infin. Dimens. Anal. Quantum Probab. Relat. Top. – volume: 116 start-page: 1563 year: 2006 end-page: 1583 ident: br000105 article-title: Weak Dirichlet processes with a stochastic control perspective publication-title: Stochastic Process. Appl. – year: 1992 ident: br000130 article-title: Introduction to the Theory of (Nonsymmetric) Dirichlet Forms – reference: G. Da Prato, A. Jentzen, M. Röckner, A mild Itô formula for SPDEs, 2011. Preprint Arxiv – year: 1996 ident: br000030 article-title: Ergodicity for Infinite-Dimensional Systems – volume: 51 start-page: 279 year: 2005 end-page: 332 ident: br000090 article-title: Generalized directional gradients, backward stochastic differential equations and mild solutions of semilinear parabolic equations publication-title: Appl. Math. Optim. – year: 2011 ident: br000095 article-title: Stochastic Differential Equations in Infinite Dimensions with Applications to Stochastic Partial Differential Equations – volume: vol. 581 start-page: 446 year: 1977 end-page: 481 ident: br000145 article-title: Notes sur les integrales stochastiques. I Intégrales hilbertiennes publication-title: Séminaire de Probabilites XI – year: 1977 ident: br000060 article-title: Vector Measures – volume: vol. 1874 start-page: 81 year: 2006 end-page: 116 ident: br000015 article-title: Natural decomposition of processes and weak Dirichlet processes publication-title: In Memoriam Paul-André Meyer: Séminaire de Probabilités XXXIX – volume: vol. 851 start-page: 476 year: 1981 end-page: 478 ident: br000085 article-title: Dirichlet processes publication-title: Stochastic Integrals (Proc. Sympos., Univ. Durham, Durham, 1980) – year: 1982 ident: br000135 article-title: Semimartingales: A Course on Stochastic Processes – year: 2007 ident: br000005 article-title: Representation and Control of Infinite Dimensional Systems – year: 1988 ident: br000115 article-title: Brownian Motion and Stochastic Calculus – volume: 97 start-page: 403 year: 1993 end-page: 421 ident: br000175 article-title: Forward, backward and symmetric stochastic integration publication-title: Probab. Theory Related Fields – year: 2000 ident: br000065 article-title: Vector Integration and Stochastic Integration in Banach Spaces – year: 1970 ident: br000195 article-title: Singular Integrals and Differentiability Properties of Functions – volume: 15 year: 2012 ident: br000050 article-title: Generalized covariation and extended Fukushima decomposition for Banach space-valued processes. Applications to windows of Dirichlet processes publication-title: Infin. Dimens. Anal. Quantum Probab. Relat. Top. – reference: G. Fabbri, F. Russo, Infinite dimensional weak Dirichlet processes, stochastic PDEs and optimal control (unpublished), 2012. Preprint – volume: 349 start-page: 209 year: 2011 end-page: 214 ident: br000045 article-title: Clark-Ocone type formula for non-semimartingales with finite quadratic variation publication-title: C. R. Acad. Sci. Paris I – volume: 10 start-page: 783 year: 2004 end-page: 827 ident: br000035 article-title: Solutions of stochastic partial differential equations considered as Dirichlet processes publication-title: Bernoulli – volume: vol. 8 start-page: 227 year: 1993 end-page: 263 ident: br000180 article-title: Noncausal stochastic integration for làd làg processes publication-title: Stochastic Analysis and Related Topics (Oslo, 1992) – reference: . – year: 1980 ident: br000140 article-title: Stochastic Integration – year: 2007 ident: br000160 article-title: Stochastic Partial Differential Equations with Lévy Noise – reference: C. Di Girolami, F. Russo, Infinite dimensional stochastic calculus via regularization, 2010. Preprint HAL-INRIA – volume: 51 year: 2014 ident: br000055 article-title: Generalized covariation for Banach space valued processes and Itô formula publication-title: Osaka J. Math. – year: 1988 ident: br000070 article-title: Linear Operators. Part I – volume: vol. 2 start-page: 1 year: 2007 end-page: 70 ident: br000120 article-title: Stochastic evolution equations publication-title: Stochastic Differential Equations: Theory and Applications – volume: 42 start-page: 890 year: 1990 end-page: 901 ident: br000125 article-title: Stochastic Fubini theorem for semimartingales in Hilbert space publication-title: Canad. J. Math. – volume: vol. 44 year: 1983 ident: br000155 publication-title: Semigroups of Linear Operators and Applications to Partial Differential Equations – volume: 35 start-page: 1438 year: 2007 end-page: 1478 ident: br000200 article-title: Stochastic integration in umd Banach spaces publication-title: Ann. Probab. – volume: 25 start-page: 307 year: 2006 end-page: 326 ident: br000110 article-title: Young integrals and SPDEs publication-title: Potential Anal. – volume: 51 start-page: 2664 issue: 3 year: 2013 ident: 10.1016/j.spa.2016.06.010_br000010 article-title: Optimal relaxed control of dissipative stochastic partial differential equations in Banach spaces publication-title: SIAM J. Control Optim. doi: 10.1137/100788574 – volume: 426 start-page: 63 year: 2004 ident: 10.1016/j.spa.2016.06.010_br000150 article-title: Uniqueness for stochastic evolution equations in Banach spaces publication-title: Dissertationes Math. (Rozprawy Mat.) – volume: vol. 44 year: 1983 ident: 10.1016/j.spa.2016.06.010_br000155 – volume: 312 start-page: 615 issue: 8 year: 1991 ident: 10.1016/j.spa.2016.06.010_br000170 article-title: Intégrales progressive, rétrograde et symétrique de processus non adaptés publication-title: C. R. Acad. Sci. Paris I – volume: 10 start-page: 783 issue: 5 year: 2004 ident: 10.1016/j.spa.2016.06.010_br000035 article-title: Solutions of stochastic partial differential equations considered as Dirichlet processes publication-title: Bernoulli – year: 1977 ident: 10.1016/j.spa.2016.06.010_br000060 – year: 2000 ident: 10.1016/j.spa.2016.06.010_br000065 – volume: 35 start-page: 1438 issue: 4 year: 2007 ident: 10.1016/j.spa.2016.06.010_br000200 article-title: Stochastic integration in umd Banach spaces publication-title: Ann. Probab. doi: 10.1214/009117906000001006 – ident: 10.1016/j.spa.2016.06.010_br000020 – volume: vol. 851 start-page: 476 year: 1981 ident: 10.1016/j.spa.2016.06.010_br000085 article-title: Dirichlet processes – year: 1988 ident: 10.1016/j.spa.2016.06.010_br000070 – year: 1982 ident: 10.1016/j.spa.2016.06.010_br000135 – year: 1992 ident: 10.1016/j.spa.2016.06.010_br000130 – volume: vol. 8 start-page: 227 year: 1993 ident: 10.1016/j.spa.2016.06.010_br000180 article-title: Noncausal stochastic integration for làd làg processes – volume: vol. 1899 start-page: 147 year: 2007 ident: 10.1016/j.spa.2016.06.010_br000185 article-title: Elements of stochastic calculus via regularization – volume: 255 start-page: 940 issue: 4 year: 2008 ident: 10.1016/j.spa.2016.06.010_br000205 article-title: Stochastic evolution equations in umd Banach spaces publication-title: J. Appl. Funct. Anal. doi: 10.1016/j.jfa.2008.03.015 – year: 1996 ident: 10.1016/j.spa.2016.06.010_br000030 – volume: 349 start-page: 209 issue: 3–4 year: 2011 ident: 10.1016/j.spa.2016.06.010_br000045 article-title: Clark-Ocone type formula for non-semimartingales with finite quadratic variation publication-title: C. R. Acad. Sci. Paris I doi: 10.1016/j.crma.2010.11.032 – year: 2011 ident: 10.1016/j.spa.2016.06.010_br000095 – ident: 10.1016/j.spa.2016.06.010_br000040 – year: 1970 ident: 10.1016/j.spa.2016.06.010_br000195 – volume: 15 issue: 2 year: 2012 ident: 10.1016/j.spa.2016.06.010_br000050 article-title: Generalized covariation and extended Fukushima decomposition for Banach space-valued processes. Applications to windows of Dirichlet processes publication-title: Infin. Dimens. Anal. Quantum Probab. Relat. Top. doi: 10.1142/S0219025712500075 – ident: 10.1016/j.spa.2016.06.010_br000080 – volume: 116 start-page: 1530 issue: 11 year: 2006 ident: 10.1016/j.spa.2016.06.010_br000100 article-title: Verification theorems for stochastic optimal control problems via a time dependent Fukushima-Dirichlet decomposition publication-title: Stochastic Process. Appl. doi: 10.1016/j.spa.2006.04.008 – volume: vol. 581 start-page: 446 year: 1977 ident: 10.1016/j.spa.2016.06.010_br000145 article-title: Notes sur les integrales stochastiques. I Intégrales hilbertiennes – volume: 18 start-page: 1550005 issue: 1 year: 2015 ident: 10.1016/j.spa.2016.06.010_br000165 article-title: Forward integration, convergence and non-adapted pointwise multipliers publication-title: Infin. Dimens. Anal. Quantum Probab. Relat. Top. doi: 10.1142/S0219025715500058 – volume: 51 issue: 3 year: 2014 ident: 10.1016/j.spa.2016.06.010_br000055 article-title: Generalized covariation for Banach space valued processes and Itô formula publication-title: Osaka J. Math. – volume: 97 start-page: 403 issue: 3 year: 1993 ident: 10.1016/j.spa.2016.06.010_br000175 article-title: Forward, backward and symmetric stochastic integration publication-title: Probab. Theory Related Fields doi: 10.1007/BF01195073 – volume: vol. 1874 start-page: 81 year: 2006 ident: 10.1016/j.spa.2016.06.010_br000015 article-title: Natural decomposition of processes and weak Dirichlet processes – volume: 42 start-page: 890 issue: 5 year: 1990 ident: 10.1016/j.spa.2016.06.010_br000125 article-title: Stochastic Fubini theorem for semimartingales in Hilbert space publication-title: Canad. J. Math. doi: 10.4153/CJM-1990-046-8 – volume: vol. 2 start-page: 1 year: 2007 ident: 10.1016/j.spa.2016.06.010_br000120 article-title: Stochastic evolution equations – year: 1980 ident: 10.1016/j.spa.2016.06.010_br000140 – volume: 116 start-page: 1563 issue: 11 year: 2006 ident: 10.1016/j.spa.2016.06.010_br000105 article-title: Weak Dirichlet processes with a stochastic control perspective publication-title: Stochastic Process. Appl. doi: 10.1016/j.spa.2006.04.009 – year: 2007 ident: 10.1016/j.spa.2016.06.010_br000005 – year: 1988 ident: 10.1016/j.spa.2016.06.010_br000115 – volume: 104 start-page: 259 issue: 2 year: 2003 ident: 10.1016/j.spa.2016.06.010_br000075 article-title: n-covariation, generalized Dirichlet processes and calculus with respect to finite cubic variation processes publication-title: Stochastic Process. Appl. doi: 10.1016/S0304-4149(02)00238-7 – year: 1992 ident: 10.1016/j.spa.2016.06.010_br000025 – volume: 51 start-page: 279 issue: 3 year: 2005 ident: 10.1016/j.spa.2016.06.010_br000090 article-title: Generalized directional gradients, backward stochastic differential equations and mild solutions of semilinear parabolic equations publication-title: Appl. Math. Optim. doi: 10.1007/s00245-004-0814-x – year: 2002 ident: 10.1016/j.spa.2016.06.010_br000190 – volume: 25 start-page: 307 issue: 4 year: 2006 ident: 10.1016/j.spa.2016.06.010_br000110 article-title: Young integrals and SPDEs publication-title: Potential Anal. doi: 10.1007/s11118-006-9013-5 – year: 2007 ident: 10.1016/j.spa.2016.06.010_br000160 |
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| SubjectTerms | Calculus via regularization Convolution type processes Covariation and quadratic variation Dirichlet processes Generalized Fukushima decomposition Infinite dimensional analysis Mathematics Probability Stochastic partial differential equations Tensor analysis |
| Title | Infinite dimensional weak Dirichlet processes and convolution type processes |
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