Maximum Principles for Partially Observed Controls of Forward SPDEs and Backward SDEs with Jumps
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918364137390080 |
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| author | Qian, Hongjiang Yin, George Cao, Yanzhao Zhang, Guannan |
| author_facet | Qian, Hongjiang Yin, George Cao, Yanzhao Zhang, Guannan |
| contents | This work establishes two versions of the Pontryagin-type maximum principles for partially observed optimal control of coupled forward stochastic partial differential equations (FSPDEs) and backward stochastic differential equations (BSDEs) with jumps in convex control domains. The FSPDE-BSDE system is driven by cylindrical Wiener processes, finite-dimensional Brownian motions, and compensated Poisson random measures. For systems with deterministic coefficients, a direct method is employed and particular attention is focused on establishing the well-posedness of a singular backward SPDE with jumps. For systems with random coefficients, a Malliavin calculus approach is developed. The main novelty here is the establishment of the well-posedness of an operator-valued SPDE with jumps, which provides a new stochastic flow representation for linear SPDEs with jumps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01188 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Maximum Principles for Partially Observed Controls of Forward SPDEs and Backward SDEs with Jumps Qian, Hongjiang Yin, George Cao, Yanzhao Zhang, Guannan Optimization and Control Probability 93E11, 93C41, 93E20, 60H15, 60H07 This work establishes two versions of the Pontryagin-type maximum principles for partially observed optimal control of coupled forward stochastic partial differential equations (FSPDEs) and backward stochastic differential equations (BSDEs) with jumps in convex control domains. The FSPDE-BSDE system is driven by cylindrical Wiener processes, finite-dimensional Brownian motions, and compensated Poisson random measures. For systems with deterministic coefficients, a direct method is employed and particular attention is focused on establishing the well-posedness of a singular backward SPDE with jumps. For systems with random coefficients, a Malliavin calculus approach is developed. The main novelty here is the establishment of the well-posedness of an operator-valued SPDE with jumps, which provides a new stochastic flow representation for linear SPDEs with jumps. |
| title | Maximum Principles for Partially Observed Controls of Forward SPDEs and Backward SDEs with Jumps |
| topic | Optimization and Control Probability 93E11, 93C41, 93E20, 60H15, 60H07 |
| url | https://arxiv.org/abs/2603.01188 |