LP Based Bounds for Cesàro and Abel Limits of the Optimal Values in Non-ergodic Stochastic Systems

Abstract

In this paper, we study asymptotic properties of problems of control of stochastic discrete time systems with time averaging and time discounting optimality criteria, and we establish that the Cesàro and Abel limits of the optimal values in such problems can be estimated with the help of a certain infinite-dimensional (ID) linear programming (LP) problem and its dual.