Abstract
This chapter is devoted to jump Markov processes and finite semi-Markov processes. In both cases, the index is considered as the calender time, continuously counted over the positive real line. Markov processes are continuous-time processes that share the Markov property with the discrete-time Markov chains. Their future evolution conditional to the past depends only on the last occupied state. Their extension to the so-called semi-Markov processes naturally arises in many types of applications. The future evolution of a semi-Markov process given the past depends on the occupied state too, but also on the time elapsed since the last transition.
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