| Issue |
ESAIM: COCV
Volume 30, 2024
|
|
|---|---|---|
| Article Number | 12 | |
| Number of page(s) | 42 | |
| DOI | https://doi.org/10.1051/cocv/2023086 | |
| Published online | 28 February 2024 | |
Optimal Control of Infinite-Dimensional Differential Systems with Randomness and Path-Dependence and Stochastic Path-Dependent Hamilton–Jacobi Equations
Department of Mathematics & Statistics, University of Calgary, 2500 University Drive NW, Calgary AB T2N 1N4, Canada
* Corresponding author: yang.yang1@ucalgary.ca
Received:
13
December
2022
Accepted:
27
November
2023
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.
Mathematics Subject Classification: 49L20 / 49L25 / 93E20 / 35D40 / 60H15
Key words: Stochastic path-dependent Hamilton-Jacobi equation / stochastic optimal control / viscosity solution / backward stochastic partial differential equation
© The authors. Published by EDP Sciences, SMAI 2024
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