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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.08277 |
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| _version_ | 1866914913490829312 |
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| author | Ning, Ning Wu, Jing Xu, Xiaoyan |
| author_facet | Ning, Ning Wu, Jing Xu, Xiaoyan |
| contents | In this paper, we study a very general stochastic variational inequality(SVI) having jumps, random coefficients, delay, and path dependence, in infinite dimensions. Well-posedness in terms of the existence and uniqueness of a solution is established, and a stochastic averaging principle on strong convergence of a time-explosion SVI to an averaged equation is obtained, both under non-Lipschitz conditions. We illustrate our results on general but concrete examples of finite dimension and infinite dimension respectively, which cover large classes of particle systems with electro-static repulsion, nonlinear stochastic partial differential equations with jumps, semilinear stochastic partial differential equations (especially stochastic reaction-diffusion equations) with delays, and others. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08277 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solutions and stochastic averaging for delay-path-dependent stochastic variational inequalities in infinite dimensions Ning, Ning Wu, Jing Xu, Xiaoyan Probability In this paper, we study a very general stochastic variational inequality(SVI) having jumps, random coefficients, delay, and path dependence, in infinite dimensions. Well-posedness in terms of the existence and uniqueness of a solution is established, and a stochastic averaging principle on strong convergence of a time-explosion SVI to an averaged equation is obtained, both under non-Lipschitz conditions. We illustrate our results on general but concrete examples of finite dimension and infinite dimension respectively, which cover large classes of particle systems with electro-static repulsion, nonlinear stochastic partial differential equations with jumps, semilinear stochastic partial differential equations (especially stochastic reaction-diffusion equations) with delays, and others. |
| title | Solutions and stochastic averaging for delay-path-dependent stochastic variational inequalities in infinite dimensions |
| topic | Probability |
| url | https://arxiv.org/abs/2408.08277 |