SINGULAR PERTURBATIONS IN STOCHASTIC ERGODIC CONTROL PROBLEMS

In this article we give a new method for studying the singular perturbations in stochastic ergodic control problems. Our method enable us to prove the convergence of the solution pair of the singularly perturbed ergodic HJB equation to the solution pair of the limiting ergodic HJB equation. In particular, the convergence of the ergodic value of the singularly perturbed ergodic control problem to that of the limiting ergodic control problem under more general conditions