Stochastic averaging principle for distribution dependent stochastic differential equations. (March 2022)

• Record Type: Journal Article
• Authors: Shen, Guangjun; Song, Jie; Wu, Jiang-Lun
• Is Part Of: Applied mathematics letters. Volume 125(2022)
• Publication Date: 2022-03
• Subjects: Stochastic averaging principle -- Distribution dependent stochastic differential equations -- Wasserstein distance; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2021.107761
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: Due to the intrinsic link with (kinetic) nonlinear Fokker–Planck equations and many diverse applications, distribution dependent stochastic differential equations have been investigated intensively in recent years. The appearance of the probability distributions (or laws) of the random variables of solutions in the coefficients is a distinct feature of distribution dependent stochastic differential equations. In this paper, under certain averaging conditions, we establish a stochastic averaging principle for distribution dependent stochastic differential equations.