Strong convergence order for slow-fast McKean-Vlasov stochastic differential equations

Abstract

In this paper, we consider the averaging principle for a class of McKean-Vlasov stochastic differential equations with slow and fast time-scales. Under some proper assumptions on the coefficients, we first prove that the slow component strongly converges to the solution of the corresponding averaged equation with convergence order $1/3$ using the approach of time discretization. Furthermore, under stronger regularity conditions on the coefficients, we use the technique of Poisson equation to improve the order to $1/2$, which is the optimal order of strong convergence in general.

33 pages. We revised some typos and added some references in the previous version

References in corpus (2)

• On the Poisson equation and diffusion approximation 3
• Strong and weak convergence in the averaging principle for SDEs with Hölder coefficients