The Annals of Probability

On Stationarity and Superposition of Point Processes

B. D. Ripley

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Abstract

This paper applies ideas from random set theory to simple point processes. We show stationarity of the hitting distributions suffices for the strict stationarity of a simple point process, but that in general all forms of stationarity differ. We compare and contrast the superposition operations of summation for random measures and union for random sets, specialized to point processes. Finally we consider completely random sets and their factors.

Article information

Source
Ann. Probab., Volume 4, Number 6 (1976), 999-1005.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995943

Digital Object Identifier
doi:10.1214/aop/1176995943

Mathematical Reviews number (MathSciNet)
MR474496

Zentralblatt MATH identifier
0359.60067

JSTOR
links.jstor.org

Subjects
Primary: 60G99: None of the above, but in this section

Keywords
Point processes random sets superposition stationary point processes infinitely divisible completely random

Citation

Ripley, B. D. On Stationarity and Superposition of Point Processes. Ann. Probab. 4 (1976), no. 6, 999--1005. doi:10.1214/aop/1176995943. https://projecteuclid.org/euclid.aop/1176995943


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