Distribution Dependent Stochastic Differential Equations

2020/12/26 by Xing Huang, Huang, Xing, Panpan Ren +3 · 8 citations
Economics, Econometrics and Finance · Mathematics · #60B05 #60B10 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2012.13656

openalex publication_date 2020/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs for short) 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.

Citations

• Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality
• Distribution dependent SDEs with singular coefficients
• Distribution dependent SDEs for Landau type equations

Cited by

• Extinction, explosion and contraction for time-inhomogeneous SDEs with jumps
• Ergodicity of conditional McKean-Vlasov jump diffusions
• The adaptive EM schemes for McKean-Vlasov SDEs with common noise in finite and infinite horizons
• Well-posedness for path-dependent multivalued McKean-Vlasov stochastic differential equations
• Analysis of mean field games via Fokker-Planck-Kolmogorov equations: existence of equilibria
• Exponential Ergodicity for McKean-Vlasov SDEs with Singular Interactions
• Distribution Dependent Birth-Death Processes: \mathbbW_p-Estimate, Ergodicity and Propagation of Chaos
• Strong Feller Regularisation of 1-d Nonlinear Transport by Reflected Ornstein-Uhlenbeck Noise

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