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.
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