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

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 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.