Poisson Thinning by Monotone Factors

Karen Ball (Indiana University, USA)

Abstract


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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Pages: 60-69

Publication Date: April 16, 2005

DOI: 10.1214/ECP.v10-1134

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