Let Xn be an irreducible aperiodic recurrent Markov chain with countable state space I and with the mean recurrence times having second moments. There is proved a global central limit theorem for the properly normalized sojourn times. More precisely, if t(n)i=Σnk=1 íi(Xk), then the probability measures induced by {t(n)i/√n−√nπi}iεI(πi being the ergotic distribution) on the Hilbert-space of square summable I-sequences converge weakly in this space to a Gaussian measure determined by a certain weak potential operator.

Bolthausen, E (1979). *A central limit theorem for the sojourn times of strongly ergodic Markov chains.* Stochastic Processes and their Applications, 9(2):217-222.

## Abstract

Let Xn be an irreducible aperiodic recurrent Markov chain with countable state space I and with the mean recurrence times having second moments. There is proved a global central limit theorem for the properly normalized sojourn times. More precisely, if t(n)i=Σnk=1 íi(Xk), then the probability measures induced by {t(n)i/√n−√nπi}iεI(πi being the ergotic distribution) on the Hilbert-space of square summable I-sequences converge weakly in this space to a Gaussian measure determined by a certain weak potential operator.

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## Additional indexing

Item Type: | Journal Article, refereed, original work |
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Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Uncontrolled Keywords: | Central limit theorem; weak convergence; sojourn times; strongly ergodic Markov chains |

Language: | English |

Date: | November 1979 |

Deposited On: | 30 Oct 2009 15:39 |

Last Modified: | 05 Apr 2016 13:30 |

Publisher: | Elsevier |

ISSN: | 0304-4149 |

Free access at: | Publisher DOI. An embargo period may apply. |

Publisher DOI: | https://doi.org/10.1016/0304-4149(79)90033-4 |

Related URLs: | http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0412.60027 |

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