A subexponential upper bound for entropy convergence of Markov chains with a spectral gap
type: Item
instance of: scholarly article
title: A subexponential upper bound for entropy convergence of Markov chains with a spectral gap
zbMATH Open document ID: 0929.60049
DOI: 10.1016/S0246-0203(99)80013-2
author: Laurent Miclo
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 2000-01-16T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77630
review text: Let \(P\) be a Markov kernel on a measurable space \(S\) with an invariant probability \(\mu\). Let \(P^*\) be the adjoint operator of \(P\) on \(L_2(\mu)\). It is assumed that the operator \(I-PP^*\) possesses a spectral gap. It is shown that this assumption implies some estimates of the speed of convergence to zero of the entropy \(\text{Ent}(P^nm\mid\mu)\), \(n\to\infty\), where \(m\) is a given probability on \(S\) satisfying certain integrability conditions, and the action \(P^nm\) is defined in a natural way. A modification of this approach is used also for some inhomogeneous Markov chains.
Mathematics Subject Classification ID: 60J27
Mathematics Subject Classification ID: 47A35
Mathematics Subject Classification ID: 47A50
Mathematics Subject Classification ID: 47A75
Mathematics Subject Classification ID: 60J10
zbMATH DE Number: 1295508
zbMATH Keywords: Markov chain
zbMATH Keywords: spectral gap
zbMATH Keywords: entropy
zbMATH Keywords: ergodicity
reviewed by: Anatoly N. Kochubei
MaRDI profile type: Publication
OpenAlex ID: W2070244396
description: scientific article; zbMATH DE number 1295508