Subgeometric Rates of Convergence for Discrete Time Markov Chains under Discrete Time Subordination

Abstract

In this note, we are concerned with the subgeometric rate of convergence of a Markov chain with discrete time parameter to its invariant measure in the $f$-norm. We clarify how three typical subgeometric rates of convergence are inherited under a discrete time version of Bochner's subordination. The crucial point is to establish the corresponding moment estimates for discrete time subordinators under some reasonable conditions on the underlying Bernstein function.

to appear in J. Theor. Probab

References in corpus (4)

• Subgeometric ergodicity of strong Markov processes
• On Shift Harnack Inequalities for Subordinate Semigroups and Moment Estimates for Lévy Processes
• Existence and estimates of moments for Lévy-type processes
• Subgeometric rates of convergence for Markov processes under subordination