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arXiv · 2501.15416

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

Jun Ma
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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.

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Jun Ma. 2025-01-26. Periodic solutions for McKean-Vlasov SDEs under periodic distribution-dependent Lyapunov conditions. https://arxiv.org/abs/2501.15416

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