PERTURBATION AND STABILITY BOUNDS FOR ERGODIC GENERAL STATE MARKOV CHAINS WITH RESPECT TO VARIOUS NORMS

This paper provides new perturbation bounds for general state Markov chains with respect to various norms. The transition and stationary characteristics estimates are given in terms of the generalized norm ergodicity coefficient, the norm of a residual kernel, or the parameters given in some drift condition. In fact, those results improve and generalize, for general state-space with respect to various norms and for a more large amplitude of perturbation of the transition kernel, the bounds obtained in [1, 32, 40]. Furthermore, we improve some other inequalities established in [22, 39, 41]. Theoretical comparison and on the basis of some examples show the quality of the results obtained in this paper.