Anticipated backward stochastic evolution equations and maximum principle for path-dependent systems in infinite dimensions
Optimization and Control
2025-11-07 v3
Abstract
For a class of path-dependent stochastic evolution equations driven by cylindrical -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.
Cite
@article{arxiv.2504.18798,
title = {Anticipated backward stochastic evolution equations and maximum principle for path-dependent systems in infinite dimensions},
author = {Guomin Liu and Jian Song and Meng Wang},
journal= {arXiv preprint arXiv:2504.18798},
year = {2025}
}