Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.18798 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914139832582144 |
|---|---|
| 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 |