Regular perturbation of V -geometrically ergodic Markov chains

Déborah Ferré (1, 2) , Loïc Hervé (1, 2) , James Ledoux (1, 2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 INSA Rennes - Institut National des Sciences Appliquées - Rennes

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 i.i.d. noises (with a non-standard probability density function) is obtained.

Mots clés: Stability; Spectral method

Domaines: Probabilités [math.PR]

Déborah Ferré, Loïc Hervé, James Ledoux. Regular perturbation of V -geometrically ergodic Markov chains. Journal of Applied Probability, 2013, 50 (1), pp.184-194. ⟨hal-00704685v2⟩