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Characterization and sufficient conditions for normed ergodicity of Markov chains

Part of: Operations research and management science Markov processes

Published online by Cambridge University Press:  01 July 2016

A. A. Borovkov  and
A. Hordijk
A. A. Borovkov*
Affiliation:
Sobolev Institute of Mathematics, Novosibirsk
A. Hordijk*
Affiliation:
Leiden University
*
∗ Postal address: Sobolev Institute of Mathematics, Koptjug pr. 4, 630090 Novosibirsk, Russia. Email address: borovkov@math.nsc.ru
∗∗ Postal address: Mathematical Institute, Leiden University, PO Box 9512, 2300 RA Leiden, The Netherlands. Email address: hordijk@math.leidenuniv.nl
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Abstract

Normed ergodicity is a type of strong ergodicity for which convergence of the nth step transition operator to the stationary operator holds in the operator norm. We derive a new characterization of normed ergodicity and we clarify its relation with exponential ergodicity. The existence of a Lyapunov function together with two conditions on the uniform integrability of the increments of the Markov chain is shown to be a sufficient condition for normed ergodicity. Conversely, the sufficient conditions are also almost necessary.

Keywords

Markov chainnormed ergodicityLyapunov function

MSC classification

Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 90B22: Queues and service
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 36 , Issue 1 , March 2004 , pp. 227 - 242
Copyright
Copyright © Applied Probability Trust 2004 

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