scholarly journals Trivial influences: A doubly stochastic poisson process model permits the detection of arbitrarily small electromagnetic signals

1995 ◽  
Vol 16 (1) ◽  
pp. 2-8 ◽  
Author(s):  
William F. Pickard
Keyword(s):  
Poisson Process ◽  
Process Model ◽  
Doubly Stochastic ◽  
Doubly Stochastic Poisson Process ◽  
Electromagnetic Signals

scholarly journals Poisson approximation for some point processes in reliability

2004 ◽  
Vol 36 (2) ◽  
pp. 455-470 ◽  
Author(s):  
Jean-Bernard Gravereaux ◽  
James Ledoux
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Point Processes ◽  
Poisson Approximation ◽  
Arrival Process ◽  
Homogeneous Poisson Process ◽  
Doubly Stochastic ◽  
Doubly Stochastic Poisson Process ◽  
Finite Markov Process ◽  
Failure Point

In this paper, we consider a failure point process related to the Markovian arrival process defined by Neuts. We show that it converges in distribution to a homogeneous Poisson process. This convergence takes place in the 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.

scholarly journals Poisson approximation for some point processes in reliability

2004 ◽  
Vol 36 (02) ◽  
pp. 455-470
Author(s):  
Jean-Bernard Gravereaux ◽  
James Ledoux
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Point Processes ◽  
Poisson Approximation ◽  
Arrival Process ◽  
Homogeneous Poisson Process ◽  
Doubly Stochastic ◽  
Doubly Stochastic Poisson Process ◽  
Finite Markov Process ◽  
Failure Point

In this paper, we consider a failure point process related to the Markovian arrival process defined by Neuts. We show that it converges in distribution to a homogeneous Poisson process. This convergence takes place in the 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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