Analysis of a discretization of a distributed control problem with a stochastic evolution equation

TL;DR

This paper investigates a discretization approach for a stochastic parabolic optimal control problem with control-dependent diffusion, establishing convergence results and introducing a Monte-Carlo method for solution approximation.

Contribution

It provides the first convergence analysis for discretizations of control problems with control-dependent diffusion terms and proposes a Monte-Carlo method for practical computation.

Findings

Convergence of the discretization is rigorously established.

A Monte-Carlo method is successfully applied to approximate solutions.

The approach handles rough data in stochastic control problems.

Abstract

This paper analyzes a discretization of a stochastic parabolic optimal control problem, where the diffusion term contains the control variable. With rough data, the convergence of the discretization is derived. In addition, a Monte-Carlo method is presented.