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Markov chains with marked transitions. (English) Zbl 0932.60078

Summary: Several useful point processes such as the Markovian arrival process, the input and departure processes of finite-capacity Markovian queues, and various models for counters and biological phenomena are obtained by considering Markov chains with marked transitions. This point of view yields many examples of interesting dependent point processes and provides a unified formalism for their study. This paper presents some characterizations of Markov chains with marked transitions.

MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60J27 Continuous-time Markov processes on discrete state spaces
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