TITLE:
Stability Estimation for Markov Control Processes with Discounted Cost
AUTHORS:
Jaime Eduardo Martínez-Sánchez
KEYWORDS:
Discrete-Time Markov Control Process, Expected Total Discounted Cost, Stability Index, Probabilistic Metric, Lévy-Prokhorov Metric
JOURNAL NAME:
Applied Mathematics,
Vol.11 No.6,
June
22,
2020
ABSTRACT: This article explores controllable Borel spaces, stationary, homogeneous Markov processes, discrete time with infinite horizon, with bounded cost functions and using the expected total discounted cost criterion. The problem of the estimation of stability for this type of process is set. The central objective is to obtain a bounded stability index expressed in terms of the Lévy-Prokhorov metric; likewise, sufficient conditions are provided for the existence of such inequalities.