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Asymptotic independence of counts in isotropic planar point processes of phase-type

Part of: Probability theory on algebraic and topological structures

Published online by Cambridge University Press:  01 July 2016

Marie-Ange Remiche
Marie-Ange Remiche*
Affiliation:
Université Libre de Bruxelles
*
∗ Postal address: Département d'Informatique, Université Libre de Bruxelles, CP 212, Blvd de Triomphe, 50, 81050 Bruxelles, Belgium. Email address: mremiche@ulb.ac.be
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Abstract

The isotropic planar point processes of phase-type are natural generalizations of the Poisson process on the plane. On the one hand, those processes are isotropic and stationary for the mean count, as in the case of the Poisson process. On the other hand, they exhibit dependence of counts in disjoint sets. In a recent paper, we have proved that the number of points in a square window has a Poisson distribution asymptotically as the window is located far away from the origin of the process. We extend our work to the case of a window of arbitrary shape.

Keywords

MAP processesmatrix-analytic methodsplanar point processes

MSC classification

Secondary: 60B10: Convergence of probability measures
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 32 , Issue 2 , June 2000 , pp. 363 - 375
Copyright
Copyright © Applied Probability Trust 2000 

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