Markov chains with marked transitions11This research was supported in part by Grant No. DMI-930628 from the National Science Foundation and the K.C. Wang Education Foundation.

AbstractSeveral 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