Anticipated backward stochastic evolution equations and maximum principle for path-dependent systems in infinite dimensions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914139832582144 |
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| author | Liu, Guomin Song, Jian Wang, Meng |
| author_facet | Liu, Guomin Song, Jian Wang, Meng |
| contents | For a class of path-dependent stochastic evolution equations driven by cylindrical $Q$-Wiener process, we study the Pontryagin's maximum principle for the stochastic recursive optimal control problem. In this infinite-dimensional control system, the state process depends on its past trajectory, the control is delayed via an integral with respect to a general finite measure, and the final cost relies on the delayed state.To obtain the maximum principle, we introduce a functional adjoint operator for the non-anticipative path derivative and establish the well-posedness of an anticipated backward stochastic evolution equation in the path-dependent form, which serves as the adjoint equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18798 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Anticipated backward stochastic evolution equations and maximum principle for path-dependent systems in infinite dimensions Liu, Guomin Song, Jian Wang, Meng Optimization and Control For a class of path-dependent stochastic evolution equations driven by cylindrical $Q$-Wiener process, we study the Pontryagin's maximum principle for the stochastic recursive optimal control problem. In this infinite-dimensional control system, the state process depends on its past trajectory, the control is delayed via an integral with respect to a general finite measure, and the final cost relies on the delayed state.To obtain the maximum principle, we introduce a functional adjoint operator for the non-anticipative path derivative and establish the well-posedness of an anticipated backward stochastic evolution equation in the path-dependent form, which serves as the adjoint equation. |
| title | Anticipated backward stochastic evolution equations and maximum principle for path-dependent systems in infinite dimensions |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2504.18798 |