Regular perturbation of V -geometrically ergodic Markov chains

TL;DR

This paper develops new stability conditions for V-geometrically ergodic Markov chains using an extended perturbation theory, providing insights into their regularity and an asymptotic expansion for specific autoregressive models.

Contribution

It introduces novel conditions for stability and regularity of V-geometrically ergodic Markov chains based on an extension of Keller and Liverani's perturbation theory.

Findings

Established new stability conditions for V-geometrically ergodic Markov chains.

Proved continuity and higher regularity properties of the invariant measure.

Derived an asymptotic expansion for an autoregressive model with non-standard noise.

Abstract

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.