Markov and Semi-Markov Processes

Valérie Girardin and Nikolaos Limnios
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Valérie Girardin: Université de Caen Normandie, Laboratoire de Mathématiques Nicolas Oresme
Nikolaos Limnios: Université de Technologie de Compiègne, Laboratoire de Mathématiques Appliquées de Compiègne

Chapter 5 in Applied Probability, 2018, pp 215-252 from Springer

Abstract: 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.

Keywords: Jump Markov Process; Occupied State; Embedded Chain; Markov Renewal; semi-Markov Kernel (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/978-3-319-97412-5_5

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