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.

Key words： Distribution dependent stochastic differential equation (DDSDE); nonlinear Fokker-Planck equation; Bismut formula; Wasserstein distance; gradient estimate

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