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December, 1976 On Stationarity and Superposition of Point Processes
B. D. Ripley
Ann. Probab. 4(6): 999-1005 (December, 1976). DOI: 10.1214/aop/1176995943

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.

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B. D. Ripley. "On Stationarity and Superposition of Point Processes." Ann. Probab. 4 (6) 999 - 1005, December, 1976. https://doi.org/10.1214/aop/1176995943

Information

Published: December, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0359.60067
MathSciNet: MR474496
Digital Object Identifier: 10.1214/aop/1176995943

Subjects:
Primary: 60G99

Keywords: completely random , Infinitely divisible , Point processes , random sets , stationary point processes , superposition

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 6 • December, 1976
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