Translator Disclaimer
February 2007 Poisson limits of sums of point processes and a particle-survivor model
Matthew O. Jones, Richard F. Serfozo
Ann. Appl. Probab. 17(1): 265-283 (February 2007). DOI: 10.1214/105051606000000763

Abstract

We present sufficient conditions for sums of dependent point processes to converge in distribution to a Poisson process. This extends the classical result of Grigelionis [Theory Probab. Appl. 8 (1963) 172–182] for sums of uniformly null point processes that have Poisson limits. Included is an application in which a particle-survivor point process converges to a Poisson process. This result sheds light on the “surprising” Poisson limit of the species competition process of Durrett and Limic [Stochastic Process. Appl. 102 (2002) 301–309].

Citation

Download Citation

Matthew O. Jones. Richard F. Serfozo. "Poisson limits of sums of point processes and a particle-survivor model." Ann. Appl. Probab. 17 (1) 265 - 283, February 2007. https://doi.org/10.1214/105051606000000763

Information

Published: February 2007
First available in Project Euclid: 13 February 2007

zbMATH: 1134.60032
MathSciNet: MR2292587
Digital Object Identifier: 10.1214/105051606000000763

Subjects:
Primary: 60G55

Rights: Copyright © 2007 Institute of Mathematical Statistics

JOURNAL ARTICLE
19 PAGES


SHARE
Vol.17 • No. 1 • February 2007
Back to Top