Some Inequalities of the Uniform Ergodicity and Strong Stability of Homogeneous Markov Chains

2000 Mathematics Subject Classification: 60J45, 60K25

In this paper we have established some uniform and strong stability estimates for homogeneous Markov chains under mixing conditions. As a general rule, the initial parameters values of the most complex systems has approximately known (they are defined on basis statistics methods), which involve errors for the calculus of research characteristics for each studied system. For this, the stability inequalities obtained in this paper allow us to use them in order to estimate numerically the error of definition for concerned characteristics, for a small perturbations of system's parameters. As an example of application, we are interesting about the well known waiting process where we consider the perturbation for the characteristics of the system when we apply a small perturbation for the control sequence.