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In this paper, we provide a methodology for computing the probabilitydistribution of sojourn times for a wide class of Markov chains. Ourmethodology consists in writing out linear systems and matrix equations forgenerating functions involving relations with entrance times. We apply thedeveloped methodology to some classes of random walks with boundedinteger-valued jumps.

Entrance and sojourn times for Markov chains. Application to $(L,R)$-random walks