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

JOURNAL OF MULTIVARIATE ANALYSIS

卷:70

Article

Stadje, W

关键词: Markov chain;    finite state-space;    numbers of visits;    joint distribution;    generating function;    asymptotic distribution;   

DOI  :  10.1006/jmva.1999.1814

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free