Electronic Journal of Probability

Point shift characterization of Palm measures on Abelian groups

Matthias Heveling and Gunter Last

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Abstract

Our first aim in this paper is to characterize Palm measures of stationary point processes through point stationarity. This generalizes earlier results from the Euclidean case to the case of an Abelian group. While a stationary point process looks statistically the same from each site, a point stationary point process looks statistically the same from each of its points. Even in the Euclidean case our proof will simplify some of the earlier arguments. A new technical result of some independent interest is the existence of a complete countable family of matchings. Using a change of measure we will generalize our results to discrete random measures. In the Euclidean case we will finally treat general random measures by means of a suitable approximation.

Article information

Source
Electron. J. Probab., Volume 12 (2007), paper no. 5, 122-137.

Dates
Accepted: 4 February 2007
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464818476

Digital Object Identifier
doi:10.1214/EJP.v12-394

Mathematical Reviews number (MathSciNet)
MR2280261

Zentralblatt MATH identifier
1128.60004

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

Keywords
point process random measure stationarity point-stationarity Palm measure matching bijective point map

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Heveling, Matthias; Last, Gunter. Point shift characterization of Palm measures on Abelian groups. Electron. J. Probab. 12 (2007), paper no. 5, 122--137. doi:10.1214/EJP.v12-394. https://projecteuclid.org/euclid.ejp/1464818476


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