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

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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.

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

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## Additional indexing

Item Type: | Journal Article, refereed, original work |
---|---|

Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Uncontrolled Keywords: | stationary Harris recurrent Markov chain; strongly mixing; convergence rates |

Language: | English |

Date: | 1982 |

Deposited On: | 19 Oct 2009 13:46 |

Last Modified: | 05 Apr 2016 13:29 |

Publisher: | Springer |

ISSN: | 0044-3719 |

Publisher DOI: | 10.1007/BF00535716 |

Related URLs: | http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0476.60022 |

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