Conditions for the existence of the forecast horizons in discounted Markov decision processes.

This paper deals with stationary Markov Decision Processes (MDPs) with a finite and an infinite horizons and expected total discounted cost (see [1], [6] and [7]). For simplicity, in this work, we consider that both X and A are finite. We denote a Discounted Markov Decision Process (MDP) with the infinite horizon by M-infinity, and Discounted MDP with the finite horizon by M-n, where n is a positive integer. For M-infinity, we present one condition (see [5]), which ensures the existence of a positive integer N* called Forecast Horizon (FH). The knowledge of the existence of N* permits to reduce the problem of the determination of an optimal policy for M-infinity, just to the determination of an optimal policy for M-N*.