Poisson approximation for some point processes in reliability
Résumé
In this paper, we consider a failure point process related to the Markovian Arrival Process defined by Neuts. We show that it onverges in distribution to a homogeneous Poisson process. This convergence takes place in context of rare occurrences of failures. We also provide a convergence rate of the convergence in total variation of this point process using an approach developed by Kabanov, Liptser and Shiryaev for the doubly-stochastic Poisson process driven by a finite Markov process.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)
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