Stochastic Maximum Principle for Optimal Control ofPartial Differential Equations Driven by White Noise

TL;DR

This paper establishes a stochastic maximum principle for optimal control of stochastic PDEs driven by white noise, focusing on well-posedness and regularity of the associated backward equations in infinite-dimensional spaces.

Contribution

It introduces a Pontryagin-type maximum principle for stochastic PDEs with white noise, addressing the well-posedness and regularity of the adjoint backward equations in infinite-dimensional settings.

Findings

Proved a maximum principle for stochastic PDE control problems.

Analyzed well-posedness of the backward stochastic differential equation.

Studied regularity properties of the adjoint process in infinite-dimensional spaces.

Abstract

We prove a stochastic maximum principle ofPontryagin's type for the optimal control of a stochastic partial differential equationdriven by white noise in the case when the set of control actions is convex. Particular attention is paid to well-posedness of the adjoint backward stochastic differential equation and the regularity properties of its solution with values in infinite-dimensional spaces.