Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.02014 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908477716168704 |
|---|---|
| author | Jiang, Yuhang Li, Jinming Li, Shihu |
| author_facet | Jiang, Yuhang Li, Jinming Li, Shihu |
| contents | In this work, we investigate the McKean-Vlasov stochastic partial differential equations driven by Poisson random measure. By adapting the variational framework, we prove the well-posedness and large deviation principle for a class of McKean-Vlasov stochastic partial differential equations with monotone coefficients. The main results can be applied to quasi-linear McKean-Vlasov equations such as distribution dependent stochastic porous media equation and stochastic p-Laplace equation. Our proof is based on the weak convergence approach introduced by Budhiraja et al. for Poisson random measures, the time discretization procedure and relative entropy estimates. In particular, we succeed in dropping the compactness assumption of embedding in the Gelfand triple in order to deal with the case of bounded and unbounded domains in applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02014 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | McKean-Vlasov SPDEs driven by Poisson random measure: Well-posedness and large deviation principle Jiang, Yuhang Li, Jinming Li, Shihu Probability 60H15, 60F10 In this work, we investigate the McKean-Vlasov stochastic partial differential equations driven by Poisson random measure. By adapting the variational framework, we prove the well-posedness and large deviation principle for a class of McKean-Vlasov stochastic partial differential equations with monotone coefficients. The main results can be applied to quasi-linear McKean-Vlasov equations such as distribution dependent stochastic porous media equation and stochastic p-Laplace equation. Our proof is based on the weak convergence approach introduced by Budhiraja et al. for Poisson random measures, the time discretization procedure and relative entropy estimates. In particular, we succeed in dropping the compactness assumption of embedding in the Gelfand triple in order to deal with the case of bounded and unbounded domains in applications. |
| title | McKean-Vlasov SPDEs driven by Poisson random measure: Well-posedness and large deviation principle |
| topic | Probability 60H15, 60F10 |
| url | https://arxiv.org/abs/2508.02014 |