Periodic solutions for McKean-Vlasov SDEs under periodic distribution-dependent Lyapunov conditions

Abstract

In this paper, we prove the existence of periodic solutions for McKean-Vlasov SDEs under periodic distribution-dependent Lyapunov conditions, which is obtained by periodic Markov processes with state space ${\mathbb{R}}^d\times \mathcal{P}({\mathbb{R}}^d)$. Here $\mathcal{P}({\mathbb{R}}^d)$ denotes the space of probability measures on ${\mathbb{R}}^d$. In addition, we show the convergence to the periodic solution and the continuous dependence on parameters of periodic solutions for McKean-Vlasov SDEs. Finally, we provide several examples to illustrate our theoretical results.