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Markov and Semi-Markov Processes

In: Applied Probability

Author

Listed:
  • Valérie Girardin

    (Université de Caen Normandie, Laboratoire de Mathématiques Nicolas Oresme)

  • Nikolaos Limnios

    (Université de Technologie de Compiègne, Laboratoire de Mathématiques Appliquées de Compiègne)

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.

Suggested Citation

  • Valérie Girardin & Nikolaos Limnios, 2018. "Markov and Semi-Markov Processes," Springer Books, in: Applied Probability, chapter 5, pages 215-252, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-97412-5_5
    DOI: 10.1007/978-3-319-97412-5_5
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