Distribution dependent stochastic differential equations
Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs) have been intensively investigated. In this paper, we summarize some recent progresses in the study of DDSDEs, which include the correspon...
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| Published in | Frontiers of Mathematics Vol. 16; no. 2; pp. 257 - 301 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Beijing
Higher Education Press
01.04.2021
Springer Nature B.V |
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| Online Access | Get full text |
| ISSN | 1673-3452 2731-8648 1673-3576 2731-8656 |
| DOI | 10.1007/s11464-021-0920-y |
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| Abstract | Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs) have been intensively investigated. In this paper, we summarize some recent progresses in the study of DDSDEs, which include the correspondence of weak solutions and nonlinear Fokker-Planck equations, the well-posedness, regularity estimates, exponential ergodicity, long time large deviations, and comparison theorems. |
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| AbstractList | Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs) have been intensively investigated. In this paper, we summarize some recent progresses in the study of DDSDEs, which include the correspondence of weak solutions and nonlinear Fokker-Planck equations, the well-posedness, regularity estimates, exponential ergodicity, long time large deviations, and comparison theorems. |
| Author | REN, Panpan WANG, Feng-Yu HUANG, Xing |
| Author_xml | – sequence: 1 givenname: Xing surname: HUANG fullname: HUANG, Xing organization: Center for Applied Mathematics, Tianjin University, Tianjin 300072, China – sequence: 2 givenname: Panpan surname: REN fullname: REN, Panpan organization: Department of Mathematics, City University of Hong Kong, Hong Kong, China – sequence: 3 givenname: Feng-Yu surname: WANG fullname: WANG, Feng-Yu email: wangfy@tju.edu.cn organization: Center for Applied Mathematics, Tianjin University, Tianjin 300072, China |
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| Keywords | Distribution dependent stochastic differential equation (DDSDE) nonlinear Fokker-Planck equation 60B05 Bismut formula 60B10 Wasserstein distance gradient estimate |
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| SubjectTerms | Bismut formula Differential equations Distribution dependent stochastic differential equation (DDSDE) Fokker-Planck equation gradient estimate Mathematical analysis Mathematics Mathematics and Statistics nonlinear Fokker-Planck equation Survey Article Wasserstein distance |
| Title | Distribution dependent stochastic differential equations |
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