Periodic solutions for McKean-Vlasov SDEs under periodic distribution-dependent Lyapunov conditions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913667075801088 |
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| author | Ma, Jun |
| author_facet | Ma, Jun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15416 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Periodic solutions for McKean-Vlasov SDEs under periodic distribution-dependent Lyapunov conditions Ma, Jun Dynamical Systems Probability 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. |
| title | Periodic solutions for McKean-Vlasov SDEs under periodic distribution-dependent Lyapunov conditions |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2501.15416 |