Perturbation and stability bounds for ergodic general state Markov chains with respect to various norms

  • Z. Mouhoubi Édouard-Montpetit College

Abstract

This paper provides new perturbation bounds for general state Markov chains with respect to various norms. The transition and stationary char- acteristics estimates are given in terms of the generalized norm ergodic- ity 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.

Published
2021-06-20
Section
Articoli