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Joint Distributions of the Numbers of Visits for Finite-State Markov Chains

✍ Scribed by Wolfgang Stadje

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 163 KB
Volume: 70
Category: Article
ISSN: 0047-259X
DOI: 10.1006/jmva.1999.1814

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✦ Synopsis

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 N th visit to r. From the explicit expressions for the corresponding generating functions we obtain the limiting multivariate distributions as N Ä when state r becomes asymptotically absorbing and for j=1, ..., r&1 the probability of a transition from r to j is of order 1ÂN.

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