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

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  • Stadje, Wolfgang

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.

Suggested Citation

  • Stadje, Wolfgang, 1999. "Joint Distributions of the Numbers of Visits for Finite-State Markov Chains," Journal of Multivariate Analysis, Elsevier, vol. 70(2), pages 157-176, August.
    • Handle: RePEc:eee:jmvana:v:70:y:1999:i:2:p:157-176
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