arXiv:2012.13656 Abstract | arXiv Analytics

arXiv:2012.13656 [math.PR]Abstract References Reviews Resources

Distribution Dependent Stochastic Differential Equations

Published 2020-12-26Version 1

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.

Comments: 44 pages. arXiv admin note: text overlap with arXiv:2002.08652, arXiv:2010.08950

Categories: math.PR

Subjects: 60B05, 60B10

Keywords: distribution dependent stochastic differential equations, nonlinear fokker-planck equations, long time large deviations, weak solutions, regularity estimates

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