201. Regular Perturbation of V-Geometrically Ergodic Markov Chains
- Author
-
Déborah Ferré, Loïc Hervé, and James Ledoux
- Subjects
Independent and identically distributed random variables ,Statistics and Probability ,60J0 ,Markov chain ,General Mathematics ,010102 general mathematics ,Perturbation (astronomy) ,Probability density function ,spectral method ,stability ,01 natural sciences ,010104 statistics & probability ,Autoregressive model ,Applied mathematics ,Ergodic theory ,47B07 ,0101 mathematics ,Statistics, Probability and Uncertainty ,Asymptotic expansion ,Spectral method ,Mathematics - 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 independent and identically distributed noises (with a nonstandard probability density function) is obtained.
- Published
- 2013