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 Electronic Communications in Probability > Vol. 10 (2005) > Paper 7 open journal systems 


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) <= X(I), almost surely.


Full text: PDF

Pages: 60-69

Published on: April 16, 2005
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Electronic Communications in Probability. ISSN: 1083-589X