Subgeometric Rates of Convergence for Discrete-Time Markov Chains Under Discrete-Time Subordination

  • Chang-Song DengEmail author


In this paper, 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.


Rate of convergence Subordination Bernstein function Moment estimate Markov chain 

Mathematics Subject Classification (2010)

Primary 60J05 Secondary 60G50 



The author would like to thank an anonymous referee for careful reading and useful suggestions.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhanChina

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