Uniform moderate deviations of functional empirical processes of Markov chains
type: Item
instance of: scholarly article
zbMATH Open document ID: 0988.60019
author: Arnaud Guillin
publication date: 2002-02-18T00:00:00Z
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60J05
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60F99
zbMATH DE Number: 1706594
zbMATH Keywords: ergodic Markov chain
zbMATH Keywords: asymptotic estimation
MaRDI profile type: Publication
title: Uniform moderate deviations of functional empirical processes of Markov chains
published in: Probability and Mathematical Statistics
review text: Let \(\{X_j,\;j\geq 0\}\) be an ergodic Markov chain with values in a general measurable state space with transition probability \(P\) and with invariant probability measure \(\pi\). Put \(M_n(t)=b^{-1}_n\sum^{[nt]}_{j=0} (\delta_{X_j}-\pi)\) and \((M_n(t))(f)=b^{-1}_n\sum^{[nt]}_{k=0} f(X_k)\) for \(f\) bounded measurable such that \(\pi(f)=0\). The paper obtains the asymptotic estimation of \({\mathbf P}_\mu\{(M_n(\cdot)),(f)\in\cdot\}\) and relative results when \(b_n\) satisfies \(b_n/\sqrt{n}\to+\infty\), \(b_n/n\to 0\).
reviewed by: Oleg K. Zakusilo
description: scientific article; zbMATH DE number 1706594