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On the rate of convergence of Borovkov's multidimensional ergodic Markov chain

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Akio Tanikawa
Akio Tanikawa*
Affiliation:
Kanazawa University
*
∗Postal address: Faculty of Engineering, Kanazawa University, 2-40-20 Kodatsuno, Kanazawa, Ishikawa 920, Japan.
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Abstract

This paper is concerned with the multidimensional Markov chain {X(n)} = {X(x, n)}, considered by Borovkov [1], [2], [3], with the form X(n + 1) = ?(n) + ?(?(n), n), where the distribution of depends only on x. Sufficient conditions on moments of |?(x)| are established for the Markov chain {X(n)} to have rate of convergence results (i.e. geometric ergodicity or sub-geometric rates for a variety of rate functions).

Keywords

MARKOV CHAINERGODICITYRATE OF CONVERGENCE

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Research Article
Information
Journal of Applied Probability , Volume 34 , Issue 2 , June 1997 , pp. 328 - 339
Copyright
Copyright © Applied Probability Trust 1997 

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