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On the modified Palm version

Part of: Stochastic processes

Published online by Cambridge University Press:  01 February 2019

Hermann Thorisson
Hermann Thorisson*
Affiliation:
University of Iceland
*
Science Institute, University of Iceland, Dunhaga 5, 107 Reykjavik, Iceland. Email address: [email protected]
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Abstract

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The interpretation of the ‘standard’ Palm version of a stationary random measure ξ is that it behaves like ξ conditioned on containing the origin in its mass. The interpretation of the ‘modified’ Palm version is that it behaves like ξ seen from a typical location in its mass. In this paper we shall focus on the modified Palm version, comparing it with the standard version in the transparent case of mixed biased coin tosses, and then establishing a limit theorem that motivates the above interpretation in the case of random measures on locally compact second countable Abelian groups possessing Følner averaging sets.

Keywords

Random measurePalm versionshift-couplingmass-stationarity

MSC classification

Primary: 60G57: Random measures 60G55: Point processes
Secondary: 60G60: Random fields
Type
Original Article
Information
Advances in Applied Probability , Volume 50 , Issue A: Branching and Applied Probability , December 2018 , pp. 271 - 280
Copyright
Copyright © Applied Probability Trust 2018 

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