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Main Authors: Liu, Guomin, Song, Jian, Wang, Meng
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2504.18798
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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