Translator Disclaimer
December 2012 On the functional central limit theorem for reversible Markov chains with nonlinear growth of the variance
Martial Longla, Costel Peligrad, Magda Peligrad
Author Affiliations +
J. Appl. Probab. 49(4): 1091-1105 (December 2012). DOI: 10.1239/jap/1354716659

Abstract

In this paper we study the functional central limit theorem (CLT) for stationary Markov chains with a self-adjoint operator and general state space. We investigate the case when the variance of the partial sum is not asymptotically linear in n, and establish that conditional convergence in distribution of partial sums implies the functional CLT. The main tools are maximal inequalities that are further exploited to derive conditions for tightness and convergence to the Brownian motion.

Citation

Download Citation

Martial Longla. Costel Peligrad. Magda Peligrad. "On the functional central limit theorem for reversible Markov chains with nonlinear growth of the variance." J. Appl. Probab. 49 (4) 1091 - 1105, December 2012. https://doi.org/10.1239/jap/1354716659

Information

Published: December 2012
First available in Project Euclid: 5 December 2012

zbMATH: 1269.60041
MathSciNet: MR3058990
Digital Object Identifier: 10.1239/jap/1354716659

Subjects:
Primary: 60F17 , 60G05 , 60G10

Keywords: functional central limit theorem , Markov chain , Martingale approximation , maximal inequality , reversible process , tightness

Rights: Copyright © 2012 Applied Probability Trust

JOURNAL ARTICLE
15 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.49 • No. 4 • December 2012
Back to Top