Journal of Applied Probability

What is typical?

Günter Last and Hermann Thorisson

Abstract

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.

Article information

Source
J. Appl. Probab., Volume 48A (2011), 379-389.

Dates
First available in Project Euclid: 18 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1318940478

Digital Object Identifier
doi:10.1239/jap/1318940478

Mathematical Reviews number (MathSciNet)
MR2865959

Zentralblatt MATH identifier
1235.60053

Subjects
Primary: 60G57: Random measures 60G55: Point processes
Secondary: 60G60: Random fields

Keywords
Random measure typical location Poisson process point-stationarity mass-stationarity Palm measure allocation invariant transport

Citation

Last, Günter; Thorisson, Hermann. What is typical?. J. Appl. Probab. 48A (2011), 379--389. doi:10.1239/jap/1318940478. https://projecteuclid.org/euclid.jap/1318940478


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