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December, 1976 Locally Finite Random Sets: Foundations for Point Process Theory
B. D. Ripley
Ann. Probab. 4(6): 983-994 (December, 1976). DOI: 10.1214/aop/1176995941

Abstract

The foundations of point process theory are surveyed. An abstract theory motivated by applications in stochastic geometry is presented. It is shown that it is sufficient to know only which sets are measurable and which are bounded in the basic space, where we use countability hypotheses rather than topological assumptions. (The sole exception is in the construction of probabilities where pseudo-topological hypotheses are needed.) It is shown that there are close connections with the random set theories of Kendall and Matheron.

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B. D. Ripley. "Locally Finite Random Sets: Foundations for Point Process Theory." Ann. Probab. 4 (6) 983 - 994, December, 1976. https://doi.org/10.1214/aop/1176995941

Information

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

zbMATH: 0359.60066
MathSciNet: MR474478
Digital Object Identifier: 10.1214/aop/1176995941

Subjects:
Primary: 60G05
Secondary: 60B99

Keywords: avoidance functions , bounded spaces , Point processes , random sets

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 6 • December, 1976
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