Approximations of McKean–Vlasov Stochastic Differential Equations with Irregular Coefficients
The goal of this paper is to approximate two kinds of McKean–Vlasov stochastic differential equations (SDEs) with irregular coefficients via weakly interacting particle systems. More precisely, propagation of chaos and convergence rate of Euler–Maruyama scheme associated with the consequent weakly i...
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| Published in | Journal of theoretical probability Vol. 35; no. 2; pp. 1187 - 1215 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.06.2022
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0894-9840 1572-9230 |
| DOI | 10.1007/s10959-021-01082-9 |
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| Abstract | The goal of this paper is to approximate two kinds of McKean–Vlasov stochastic differential equations (SDEs) with irregular coefficients via weakly interacting particle systems. More precisely, propagation of chaos and convergence rate of Euler–Maruyama scheme associated with the consequent weakly interacting particle systems are investigated for McKean–Vlasov SDEs, where (1) the diffusion terms are Hölder continuous by taking advantage of Yamada–Watanabe’s approximation approach and (2) the drifts are Hölder continuous by freezing distributions followed by invoking Zvonkin’s transformation trick. |
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| AbstractList | The goal of this paper is to approximate two kinds of McKean–Vlasov stochastic differential equations (SDEs) with irregular coefficients via weakly interacting particle systems. More precisely, propagation of chaos and convergence rate of Euler–Maruyama scheme associated with the consequent weakly interacting particle systems are investigated for McKean–Vlasov SDEs, where (1) the diffusion terms are Hölder continuous by taking advantage of Yamada–Watanabe’s approximation approach and (2) the drifts are Hölder continuous by freezing distributions followed by invoking Zvonkin’s transformation trick. |
| Author | Bao, Jianhai Huang, Xing |
| Author_xml | – sequence: 1 givenname: Jianhai surname: Bao fullname: Bao, Jianhai organization: Center for Applied Mathematics, Tianjin University – sequence: 2 givenname: Xing orcidid: 0000-0002-0841-5230 surname: Huang fullname: Huang, Xing email: xinghuang@tju.edu.cn organization: Center for Applied Mathematics, Tianjin University |
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| Cites_doi | 10.1016/j.spa.2018.12.012 10.1007/BFb0085169 10.1214/15-AOP1076 10.1214/17-EJP25 10.1137/15M1015583 10.1090/mcom3042 10.1214/aoap/1050689593 10.1007/s10959-018-0854-9 10.1142/S0219493719500424 10.1007/s00440-017-0774-0 10.2307/1911241 10.1073/pnas.56.6.1907 10.1051/proc/201965068 10.1016/j.spa.2011.06.008 10.1214/18-EJP259 10.1090/tran/7576 10.1016/j.spa.2019.01.006 10.1016/j.spa.2017.05.006 10.1214/17-AAP1280 10.1214/19-EJP390 10.1007/978-3-319-58920-6 10.1214/18-AAP1416 |
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| Keywords | 65C30 65C35 McKean–Vlasov stochastic differential equation Zvonkin’s transformation 65C05 Hölder continuity Yamada–Watanabe approximation |
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| Title | Approximations of McKean–Vlasov Stochastic Differential Equations with Irregular Coefficients |
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