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

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## 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 $O(n^{-1/2})$.

## Citations

37 citations in Web of Science®
34 citations in Scopus®