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arXiv · 2504.18798

Anticipated backward stochastic evolution equations and maximum principle for path-dependent systems in infinite dimensions

Guomin Liu·Jian Song·Meng Wang
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Abstract

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.

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Guomin Liu, Jian Song, Meng Wang. 2025-04-26. Anticipated backward stochastic evolution equations and maximum principle for path-dependent systems in infinite dimensions. https://arxiv.org/abs/2504.18798

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