The Berry-Esseen theorem for strongly mixing Harris recurrent Markov chains

Bolthausen, E (1982). The Berry-Esseen theorem for strongly mixing Harris recurrent Markov chains. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 60(3):283-289.

Full text not available from this repository.

Abstract

Let $\xi_0,\xi_1,\cdots$ be a stationary Harris-recurrent Markov chain with state space $(E,\scr E)$ , and let $f\colon E\rightarrow{\bf R}$ and $X_i=f(\xi_i)$ . It is known that the sequence $X_i$ , $i\geq 0$ , is strongly mixing, i.e., $\alpha(n)\rightarrow 0$ , where $\alpha(n)$ are the strong (or Rosenblatt) mixing coefficients. If $\alpha(n)$ decreases at a sufficiently fast rate and $f$ is suitably chosen, then a central limit theorem holds for the partial sums $\sum_{i=0}^nX_i$ . The present paper gives conditions for the convergence rates to be $O(n^{-1/2})$ .

Item Type:	Journal Article, refereed, original work
Communities & Collections:	07 Faculty of Science > Institute of Mathematics
DDC:	510 Mathematics
Uncontrolled Keywords:	stationary Harris recurrent Markov chain; strongly mixing; convergence rates
Language:	English
Date:	1982
Deposited On:	19 Oct 2009 15:46
Last Modified:	23 Nov 2012 17:37
Publisher:	Springer
ISSN:	0044-3719
Publisher DOI:	10.1007/BF00535716
Related URLs:	http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0476.60022
WoS Citation Count:	35

Users (please log in): suggest update or correction for this item

Repository Staff Only: item control page