Distribution dependent stochastic differential equations

• Published in: Frontiers of Mathematics Vol. 16; no. 2; pp. 257 - 301
• Main Authors: HUANG, Xing, REN, Panpan, WANG, Feng-Yu
• Format: Journal Article
• Language: English
• Published: Beijing Higher Education Press 01.04.2021; Springer Nature B.V
• Subjects: 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; Distribution dependent stochastic differential equation (DDSDE); nonlinear Fokker-Planck equation; 60B05; Bismut formula; 60B10; Wasserstein distance; gradient estimate
• ISSN: 1673-3452; 2731-8648; 1673-3576; 2731-8656
• DOI: 10.1007/s11464-021-0920-y

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.