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Entrance and sojourn times for Markov chains, application to \((L, R)\)-random walks. (English) Zbl 1341.60086

Summary: In this paper, we provide a methodology for computing the probability distribution of sojourn times for a wide class of Markov chains. Our methodology consists in writing out linear systems and matrix equations for generating functions involving relations with entrance times. We apply the developed methodology to some classes of random walks with bounded integer-valued jumps.

MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60G50 Sums of independent random variables; random walks
60J22 Computational methods in Markov chains
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