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The Palm-duality for random subsets of d-dimensional grids

Part of: Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Hermann Thorisson
Hermann Thorisson*
Affiliation:
University of Iceland
*
∗ Postal address: Department of Mathematics, University of Iceland, 107 Reykjavik, Iceland. Email address: [email protected]
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Abstract

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The Palm version of a stationary random subset of a d-dimensional grid is contructed using the two-step change-of-origin and change-of-measure method. An elementary proof is given of the fact that the Palm version is characterized by point-stationarity (distributional invariance under bijective shifts of the origin from a point of the set to another point of the set).

Keywords

Palm theorypoint processesstationary random field

MSC classification

Primary: 60G55: Point processes
Secondary: 60G60: Random fields
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 39 , Issue 2 , June 2007 , pp. 318 - 325
Copyright
Copyright © Applied Probability Trust 2007 

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