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Sojourn times in finite Markov processes. (English) Zbl 0688.60059

Summary: Sojourn times of Markov processes in subsets of the finite state space are considered. We give a closed form of the distribution of the n th sojourn time in a given subset of states. The asymptotic behaviour of this distribution when time goes to infinity is analyzed, in the discrete time and the continuous-time cases.

We consider the usually pseudo-aggregated Makov process canonically constructed from the previous one by collapsing the states of each subset of a given partition. The relation between limits of moments of the sojourn time distributions is the original Markov process and the moments of the corresponding holding times of the pseudo-aggregated one is also studied.

MSC:
60J20Applications of Markov chains and discrete-time Markov processes on general state spaces
60K10Applications of renewal theory