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2005 Poisson Thinning by Monotone Factors
Karen Ball
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Electron. Commun. Probab. 10: 60-69 (2005). DOI: 10.1214/ECP.v10-1134


Let $X$ and $Y$ be Poisson point processes on the real numbers with rates $l_1$ and $l_2$ respectively. We show that if $l_1 > l_2$, then there exists a deterministic map $f$ such that $f(X)$ and $Y$ have the same distribution, the joint distribution of $(X, f(X))$ is translation-invariant, and which is monotone in the sense that for all intervals $I$, $f(X)(I) \leq X(I)$, almost surely.


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Karen Ball. "Poisson Thinning by Monotone Factors." Electron. Commun. Probab. 10 60 - 69, 2005.


Accepted: 16 April 2005; Published: 2005
First available in Project Euclid: 4 June 2016

zbMATH: 1110.60050
MathSciNet: MR2133893
Digital Object Identifier: 10.1214/ECP.v10-1134

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