Stochastic averaging principle for distribution dependent stochastic differential equations

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.