Title: Optimal Control of Infinite-Dimensional Differential Systems with Randomness and Path-Dependence and Stochastic Path-Dependent Hamilton–Jacobi Equations.
Authors: Qiu, Jinniao; Yang, Yang
Abstract: This paper is devoted to the stochastic optimal control problem of infinite-dimensional differential systems allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases studied by Bayraktar and Keller [J. Funct. Anal. 275 (2018) 2096-2161], the value function turns out to be a random field on the path space and it is characterized by a stochastic path-dependent Hamilton-Jacobi (SPHJ) equation. A notion of viscosity solution is proposed and the value function is proved to be the unique viscosity solution to the associated SPHJ equation.
Subjects: STOCHASTIC partial differential equations; STOCHASTIC control theory; HAMILTON-Jacobi equations; VISCOSITY solutions; RANDOM fields
Publication: ESAIM: Control, Optimisation & Calculus of Variations, 2024, Vol 30, p1
ISSN: 1292-8119
Publication type: Academic Journal
DOI: 10.1051/cocv/2023086

Optimal Control of Infinite-Dimensional Differential Systems with Randomness and Path-Dependence and Stochastic Path-Dependent Hamilton–Jacobi Equations.

Qiu, Jinniao; Yang, Yang