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May 1996 Poisson approximation for point processes via monotone couplings
Timothy C. Brown, Darryl Greig
Ann. Appl. Probab. 6(2): 545-560 (May 1996). DOI: 10.1214/aoap/1034968143

Abstract

Monotonicity properties of certain classes of point processes with respect to the Palm measure are exploited to derive upper and lower bounds on the total variation distance away from Poisson of these processes. The results obtained are applied to new better than used and new worse than used renewal processes and to a Cox process with rates given by a two state Markov chain.

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Timothy C. Brown. Darryl Greig. "Poisson approximation for point processes via monotone couplings." Ann. Appl. Probab. 6 (2) 545 - 560, May 1996. https://doi.org/10.1214/aoap/1034968143

Information

Published: May 1996
First available in Project Euclid: 18 October 2002

zbMATH: 0865.60037
MathSciNet: MR1398057
Digital Object Identifier: 10.1214/aoap/1034968143

Subjects:
Primary: 60G55
Secondary: 60J25 , 60K05

Keywords: Cox process , monotone couplings , NBU , NWU renewal process , Poisson approximation

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.6 • No. 2 • May 1996
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