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Deterministic thinning of finite Poisson processes
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Angel, Omer, Holroyd, Alexander E. and Soo, Terry (2010) Deterministic thinning of finite Poisson processes. Proceedings of the American Mathematical Society, Vol.139 (No.2). pp. 707-720. doi:10.1090/S0002-9939-2010-10535-X ISSN 0002-9939.
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Official URL: http://dx.doi.org/10.1090/S0002-9939-2010-10535-X
Abstract
Let Pi and Gamma be homogeneous Poisson point processes on a fixed set of finite volume. We prove a necessary and sufficient condition on the two intensities for the existence of a coupling of Pi and Gamma such that Gamma is a deterministic function of Pi, and all points of Gamma are points of Pi. The condition exhibits a surprising lack of monotonicity. However, in the limit of large intensities, the coupling exists if and only if the expected number of points is at least one greater in Pi than in Gamma.
Item Type: | Journal Article | ||||
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Alternative Title: | Omer Angel, Alexander E. Holroyd and Terry Soo | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Journal or Publication Title: | Proceedings of the American Mathematical Society | ||||
Publisher: | American Mathematical Society | ||||
ISSN: | 0002-9939 | ||||
Official Date: | August 2010 | ||||
Dates: |
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Volume: | Vol.139 | ||||
Number: | No.2 | ||||
Page Range: | pp. 707-720 | ||||
DOI: | 10.1090/S0002-9939-2010-10535-X | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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