A comparison theorem for Bellman equations of ergodic control

Abstract

The aim of this paper is to establish a comparison theorem for the Bellman equation of an ergodic control in $ \mathbb R ^d$. This comparison theorem gives a new characterization of the optimal value by sub/super--solutions of the Bellman equation. This result is applicable to compute both of lower and upper bound of the optimal value. Furthermore, from this comparison theorem, we also give a simple proof of the uniqueness result for the Bellman equation.