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- 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