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Weak homogenization of point processes by space deformations

Part of: Stochastic processes

Published online by Cambridge University Press:  01 July 2016

R. Senoussi ,
J. Chadœuf  and
D. Allard
R. Senoussi*
Affiliation:
INRA, France
J. Chadœuf*
Affiliation:
INRA, France
D. Allard*
Affiliation:
INRA, France
*
∗ Postal address: INRA, Laboratoire de Biométrie, Domaine Saint-Paul, Site Agroparc, 84 914 Avignon, Cedex 9, France.
∗ Postal address: INRA, Laboratoire de Biométrie, Domaine Saint-Paul, Site Agroparc, 84 914 Avignon, Cedex 9, France.
∗ Postal address: INRA, Laboratoire de Biométrie, Domaine Saint-Paul, Site Agroparc, 84 914 Avignon, Cedex 9, France.
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Abstract

We study the transformation of a non-stationary point process ξ on ℝn into a weakly stationary point process ͂ξ, with ͂ξ(B) = ξ(Φ-1(B)), where B is a Borel set, via a deformation Φ of the space ℝn. When the second-order measure is regular, Φ is uniquely determined by the homogenization equations of the second-order measure. In contrast, the first-order homogenization transformation is not unique. Several examples of point processes and transformations are investigated with a particular interest to Poisson processes.

Keywords

Spatial point processmoment measurehomogenizationnon-stationary point processspace transformation

MSC classification

Primary: 60G55: Point processes
Secondary: 60G12: General second-order processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 32 , Issue 4 , December 2000 , pp. 948 - 959
Copyright
Copyright © Applied Probability Trust 2000 

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