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

2025/01/26 by Jun Ma, Ma, Jun
Economics, Econometrics and Finance · #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2501.15416

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× \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.

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