Stochastic homogenization of deterministic control problems

Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK.

^* Corresponding author: Alexander.Van-Brunt@maths.ox.ac.uk

Received: 21 June 2018
Accepted: 24 February 2021

Abstract

In this paper we study homogenization of a class of control problems in a stationary and ergodic random environment. This problem has been mostly studied in the calculus of variations setting in connection to the homogenization of the Hamilton–Jacobi equation. We extend the result to control problems with more general state dynamics and macroscopically inhomogeneous Lagrangians. Moreover, our approach proves homogenization under weaker growth assumptions on the Lagrangian, even in the well-studied calculus of variations setting.