Malliavin calculus and regularity of the density of an invariant probability for a Markov chain
type: Item
instance of: scholarly article
title: Malliavin calculus and regularity of the density of an invariant probability for a Markov chain
zbMATH Open document ID: 0762.60043
author: J. B. Gravereaux
author: Agnes Coquio
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1993-02-04T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77441
review text: The authors consider Markov chains \(X_ n=\varphi(X_{n-1},Z_ n)\), \(X_ 0=x\in{\mathbf R}^ d\), which have an invariant measure \(\eta((Z_ n)\) is a sequence of independent random variables), with some conditions on the function \(\varphi\), the measure \(\eta\) and the Markov chain \((X_ n)\). Using the Malliavin's calculus on the probability space associated to \((Z_ n)\), they show that the invariant measure \(\eta\) has a density of class \(C^ p\) with respect to the Lebesgue measure. Some examples are also discussed.
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 60J05
zbMATH DE Number: 110498
zbMATH Keywords: Markov jump processes
zbMATH Keywords: invariant measure
zbMATH Keywords: Malliavin's calculus
reviewed by: J.-P. Lepeltier
MaRDI profile type: Publication
Recommended article: Q4858538
Recommended article: Calcul de Malliavin et probabilité invariante d'une chaîne de Markov. (Malliavin calculus and invariant measure of a Markov chain)
Recommended article: On the existence of invariant densities for Markov operators
Recommended article: Existence of bounded invariant probability densities for Markov chains
Recommended article: Malliavin Calculus for Stochastic Processes and Random Measures with Independent Increments
Recommended article: Invariant densities and mean ergodicity of Markov operators
Recommended article: Regularity results for infinite dimensional diffusions: A Malliavin calculus approach
description: scientific article; zbMATH DE number 110498