## Joint distributions of the numbers of visits for finite-state Markov chains

Autor(en): | Stadje, W |

Stichwörter: | asymptotic distribution; finite state-space; generating function; joint distribution; Markov chain; Mathematics; numbers of visits; Statistics & Probability |

Erscheinungsdatum: | 1999 |

Herausgeber: | ELSEVIER INC |

Journal: | JOURNAL OF MULTIVARIATE ANALYSIS |

Volumen: | 70 |

Ausgabe: | 2 |

Startseite: | 157 |

Seitenende: | 176 |

Zusammenfassung: | For a discrete-time Markov chain with finite state space {1, ..., r} we consider the joint distribution of the numbers of visits in states 1, ..., r - 1 during the first N steps or before the Nth visit to r.. From the explicit expressions for the corresponding generating Functions we obtain the limiting multivariate distributions as N --> infinity when state, becomes asymptotically absorbing and for j = 1, ..., r - 1 the probability of a transition from r to j is of order 1/N. (C) 1999 Academic Press. |

ISSN: | 0047259X |

DOI: | 10.1006/jmva.1999.1814 |

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