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Regular Perturbation of V-Geometrically Ergodic Markov Chains

Part of: Special classes of linear operators

Published online by Cambridge University Press:  30 January 2018

Déborah Ferré ,
Loïc Hervé  and
James Ledoux
Déborah Ferré*
Affiliation:
Institut National des Sciences Appliquées
Loïc Hervé*
Affiliation:
Institut National des Sciences Appliquées
James Ledoux*
Affiliation:
Institut National des Sciences Appliquées
*
∗ Postal address: Mathematical Research Institute of Rennes, Institut National des Sciences Appliquées, 20 Avenue des Buttes de Coesmes, CS 70 839, 35708 Rennes cedex 7, France.
∗ Postal address: Mathematical Research Institute of Rennes, Institut National des Sciences Appliquées, 20 Avenue des Buttes de Coesmes, CS 70 839, 35708 Rennes cedex 7, France.
∗ Postal address: Mathematical Research Institute of Rennes, Institut National des Sciences Appliquées, 20 Avenue des Buttes de Coesmes, CS 70 839, 35708 Rennes cedex 7, France.
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Abstract

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In this paper, new conditions for the stability of V-geometrically ergodic Markov chains are introduced. The results are based on an extension of the standard perturbation theory formulated by Keller and Liverani. The continuity and higher regularity properties are investigated. As an illustration, an asymptotic expansion of the invariant probability measure for an autoregressive model with independent and identically distributed noises (with a nonstandard probability density function) is obtained.

Keywords

stabilityspectral method

MSC classification

Primary: 47B07: Operators defined by compactness properties
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 1 , March 2013 , pp. 184 - 194
Copyright
Copyright © Applied Probability Trust 2013 

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