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

Wolfgang Stadje

Journal of Multivariate Analysis, 1999, vol. 70, issue 2, 157-176

Abstract: 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 firstNsteps or before theNth visit tor. From the explicit expressions for the corresponding generating functions we obtain the limiting multivariate distributions asN-->[infinity] when staterbecomes asymptotically absorbing and forj=1, ..., r-1 the probability of a transition fromrtojis of order 1/N.

Keywords: Markov; chain; finite; state-space; numbers; of; visits; joint; distribution; generating; function; asymptotic; distribution (search for similar items in EconPapers)
Date: 1999
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