Accéder directement au contenu Accéder directement à la navigation

# State-discretization of V -geometrically ergodic Markov chains and convergence to the stationary distribution

Abstract : Let $(X_n)_{n \in\mathbb{N}}$ be a $V$-geometrically ergodic Markov chain on a measurable space $\mathbb{X}$ with invariant probability distribution $\pi$. In this paper, we propose a discretization scheme providing a computable sequence $(\widehat\pi_k)_{k\ge 1}$ of probability measures which approximates $\pi$ as $k$ growths to infinity. The probability measure $\widehat\pi_k$ is computed from the invariant probability distribution of a finite Markov chain. The convergence rate in total variation of $(\widehat\pi_k)_{k\ge 1}$ to $\pi$ is given. As a result, the specific case of first order autoregressive processes with linear and non-linear errors is studied. Finally, illustrations of the procedure for such autoregressive processes are provided, in particular when no explicit formula for $\pi$ is known.
Keywords :
Type de document :
Article dans une revue
Domaine :

Littérature citée [16 références]

https://hal.archives-ouvertes.fr/hal-02306687
Contributeur : James Ledoux <>
Soumis le : lundi 7 octobre 2019 - 22:59:09
Dernière modification le : jeudi 30 juillet 2020 - 12:36:36

### Fichier

HAL-AR.pdf
Fichiers produits par l'(les) auteur(s)

### Identifiants

• HAL Id : hal-02306687, version 1

### Citation

Loïc Hervé, James Ledoux. State-discretization of V -geometrically ergodic Markov chains and convergence to the stationary distribution. Methodology and Computing in Applied Probability, Springer Verlag, 2020, 22 (3), pp.905-925. ⟨hal-02306687⟩

### Métriques

Consultations de la notice

## 135

Téléchargements de fichiers