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

被引：0
|
作者：
Qiu, Jinniao [1 ]
Yang, Yang [1 ]
机构：
[1] Univ Calgary, Dept Math & Stat, 2500 Univ Drive NW, Calgary, AB T2N 1N4, Canada
来源：
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2024年 / 30卷
关键词：
Stochastic path-dependent Hamilton-Jacobi equation; stochastic optimal control; viscosity solution; backward stochastic partial differential equation; VISCOSITY SOLUTIONS; BELLMAN EQUATIONS; UNIQUENESS;
D O I：
10.1051/cocv/2023086
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
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.
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页数：42
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