Distribution dependent stochastic differential equations

Xing Huang; Panpan Ren; Feng-Yu Wang

doi:10.1007/s11464-021-0920-y

Distribution dependent stochastic differential equations

Xing Huang, Panpan Ren, Feng-Yu Wang^*

^*Corresponding author for this work

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

49 Citations (Scopus)

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.

Original language	English
Pages (from-to)	257–301
Journal	Frontiers of Mathematics in China
Volume	16
Issue number	2
Online published	7 Apr 2021
DOIs	https://doi.org/10.1007/s11464-021-0920-y
Publication status	Published - Apr 2021

Research Keywords

60B05
60B10
Bismut formula
Distribution dependent stochastic differential equation (DDSDE)
gradient estimate
nonlinear Fokker-Planck equation
Wasserstein distance

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10.1007/s11464-021-0920-y

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title = "Distribution dependent stochastic differential equations",

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.",

keywords = "60B05, 60B10, Bismut formula, Distribution dependent stochastic differential equation (DDSDE), gradient estimate, nonlinear Fokker-Planck equation, Wasserstein distance",

author = "Xing Huang and Panpan Ren and Feng-Yu Wang",

year = "2021",

month = apr,

doi = "10.1007/s11464-021-0920-y",

language = "English",

volume = "16",

pages = "257–301",

journal = "Frontiers of Mathematics in China",

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publisher = "Higher Education Press",

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TY - JOUR

T1 - Distribution dependent stochastic differential equations

AU - Huang, Xing

AU - Ren, Panpan

AU - Wang, Feng-Yu

PY - 2021/4

Y1 - 2021/4

N2 - 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.

AB - 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.

KW - 60B05

KW - 60B10

KW - Bismut formula

KW - Distribution dependent stochastic differential equation (DDSDE)

KW - gradient estimate

KW - nonlinear Fokker-Planck equation

KW - Wasserstein distance

UR - http://www.scopus.com/inward/record.url?scp=85103625800&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85103625800&origin=recordpage

U2 - 10.1007/s11464-021-0920-y

DO - 10.1007/s11464-021-0920-y

M3 - RGC 21 - Publication in refereed journal

SN - 1673-3452

VL - 16

SP - 257

EP - 301

JO - Frontiers of Mathematics in China

JF - Frontiers of Mathematics in China

IS - 2

ER -

Distribution dependent stochastic differential equations

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Research Keywords

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