The Annals of Probability

Ramsey's Theorem and Poisson Random Measures

Timothy C. Brown and Joseph Kupka

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Abstract

Prekopa's theorem gives a qualitative sufficient condition for a completely random point process to be Poisson. A generalization of this theorem is presented. The proof is elementary and uses a combinatorial principle known as Ramsey's theorem.

Article information

Source
Ann. Probab., Volume 11, Number 4 (1983), 904-908.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993440

Digital Object Identifier
doi:10.1214/aop/1176993440

Mathematical Reviews number (MathSciNet)
MR714954

Zentralblatt MATH identifier
0533.60057

JSTOR
links.jstor.org

Subjects
Primary: 60G57: Random measures
Secondary: 05C55: Generalized Ramsey theory [See also 05D10]

Keywords
Poisson random measures Prekopa's theorem Ramsey's theorem

Citation

Brown, Timothy C.; Kupka, Joseph. Ramsey's Theorem and Poisson Random Measures. Ann. Probab. 11 (1983), no. 4, 904--908. doi:10.1214/aop/1176993440. https://projecteuclid.org/euclid.aop/1176993440


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