Weak convergence of Mckean-Vlasov stochastic differential equations with two-time-scale Markov switching

Abstract

This paper focus on Mckean-Vlasov stochastic differential equations (SDEs) with two-time-scale Markov switching. These stochastic processes include the microcosmic location, the macrocosmic distribution of particles and the discrete event. Under appropriate conditions, by using martingale method, we prove that the original system will weakly converge to the corresponding limit system as ε → 0. Finally, an example is given to illustrate our results and the conclusion and future works are presented.