Uniform Ergodicity and Strong Stability Estimates of Homogeneous Markov Chains*

Abstract

The aim of this paper is to investigate some uniform ergodicity and strong stability estimates for homogeneous markov chains, which may be considered as a refinement of those established by the authors with respect to a given weight norm. As a general rule, the initial parameter values of the most complex systems are approximately known (they are defined on the basis of statistical methods), which results in errors for the calculus of research characteristics for each studied system. For this, the uniform ergodicity and stability inequalities obtained in this paper make it possible to use them in order to estimate numerically the error of definition for the considered characteristics for small perturbations of the system’s parameters. As an example of application, we study the well-known Lindley process, and a comparison with some results obtained by Kartashov is established.