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Article Dans Une Revue Advances in Applied Probability Année : 2004

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.
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Dates et versions

hal-00837505 , version 1 (19-08-2013)

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  • HAL Id : hal-00837505 , version 1

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Jean-Bernard Gravereaux, James Ledoux. Poisson approximation for some point processes in reliability. Advances in Applied Probability, 2004, 36 (2), pp.455-470. ⟨hal-00837505⟩
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