## Electronic Communications in Probability

### Poisson Thinning by Monotone Factors

Karen Ball

#### 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.

#### Article information

Source
Electron. Commun. Probab., Volume 10 (2005), paper no. 7, 60-69.

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

https://projecteuclid.org/euclid.ecp/1465058072

Digital Object Identifier
doi:10.1214/ECP.v10-1134

Mathematical Reviews number (MathSciNet)
MR2133893

Zentralblatt MATH identifier
1110.60050

Rights

#### Citation

Ball, Karen. Poisson Thinning by Monotone Factors. Electron. Commun. Probab. 10 (2005), paper no. 7, 60--69. doi:10.1214/ECP.v10-1134. https://projecteuclid.org/euclid.ecp/1465058072

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