Occupation Times in Markov Processes

Bruno Sericola 1
1 ARMOR - Architectures and network models
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes, Ecole Nationale Supérieure des Télécommunications de Bretagne
Abstract : We consider, in a homogeneous Markov process with finite state space, the occupation times that is, the times spent by the process in given subsets of the state space during a finite interval of time. We first derive the distribution of the occupation time of one subset and then we generalize this result to the joint distribution of occupation times of different subsets of the state space by the use of order statistics from the uniform distribution. Next, we consider the distribution of weighted sums of occupation times. We obtain the forward and backward equations describing the behavior of these weighted sums and we show how these equations lead to simple expressions of this distribution.
Type de document :
Rapport
[Research Report] RR-3806, INRIA. 1999
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https://hal.inria.fr/inria-00072852
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Soumis le : mercredi 24 mai 2006 - 11:05:54
Dernière modification le : jeudi 11 janvier 2018 - 06:20:08
Document(s) archivé(s) le : dimanche 4 avril 2010 - 23:25:10

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Bruno Sericola. Occupation Times in Markov Processes. [Research Report] RR-3806, INRIA. 1999. 〈inria-00072852〉

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