Stochastic maximum principle for weighted mean-field system with jump
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916945180229632 |
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| author | Tang, Yanyan Xiong, Jie |
| author_facet | Tang, Yanyan Xiong, Jie |
| contents | In this article, we consider a weighted mean-field control problem with jump-diffusion as its state process. The main difficulty is from the non-Lipschitz property of the coefficients. We overcome this difficulty by an $L_{p,q}$-estimate of the solution processes with a suitably chosen $p$ and $q$. Convex pertubation method combining with the aforementioned $L_{p,q}$-estimation method is utilized to derive the stochastic maximum principle for this control problem. A sufficient condition for the optimality is also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16000 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic maximum principle for weighted mean-field system with jump Tang, Yanyan Xiong, Jie Optimization and Control Probability In this article, we consider a weighted mean-field control problem with jump-diffusion as its state process. The main difficulty is from the non-Lipschitz property of the coefficients. We overcome this difficulty by an $L_{p,q}$-estimate of the solution processes with a suitably chosen $p$ and $q$. Convex pertubation method combining with the aforementioned $L_{p,q}$-estimation method is utilized to derive the stochastic maximum principle for this control problem. A sufficient condition for the optimality is also given. |
| title | Stochastic maximum principle for weighted mean-field system with jump |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2403.16000 |