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What is typical?

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Günter Last  and
Hermann Thorisson
Günter Last
Affiliation:
Karlsruhe Institute of Technology, Institut für Stochastik, Karlsruhe Institute of Technology, D-76128 Karlsruhe, Germany
Hermann Thorisson
Affiliation:
University of Iceland, Science Institute, University of Iceland, Dunhaga 3, 107 Reykjavik, Iceland. Email address: hermann@hi.is
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Abstract

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Let ξ be a random measure on a locally compact second countable topological group, and let X be a random element in a measurable space on which the group acts. In the compact case we give a natural definition of the concept that the origin is a typical location for X in the mass of ξ, and prove that when this holds, the same is true on sets placed uniformly at random around the origin. This new result motivates an extension of the concept of typicality to the locally compact case where it coincides with the concept of mass-stationarity. We describe recent developments in Palm theory where these ideas play a central role.

Keywords

Random measuretypical locationPoisson processpoint-stationaritymass-stationarityPalm measureallocationinvariant transport

MSC classification

Primary: 60G57: Random measures 60G55: Point processes
Secondary: 60G60: Random fields
Type
Part 8. Point Processes
Information
Journal of Applied Probability , Volume 48 , Issue A: New Frontiers in Applied Probability (Journal of Applied Probability Special Volume 48A) , August 2011 , pp. 379 - 389
Copyright
Copyright © Applied Probability Trust 2011 

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