Poisson approximation for some point processes in reliability
Gravereaux, Jean-Bernard ; Ledoux, James
HAL, hal-00837505 / Harvested from HAL
Text on HAL
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.
Publié le : 2004-07-05
Classification:  AMS 60G55; 60J25; 60J75; 90B25; 93E11,  [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 
@article{hal-00837505,
     author = {Gravereaux, Jean-Bernard and Ledoux, James},
     title = {Poisson approximation for some point processes in reliability},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00837505}
}

Gravereaux, Jean-Bernard; Ledoux, James. Poisson approximation for some point processes in reliability. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00837505/