Poisson limits of sums of point processes and a particle-survivor model
Probability
2007-05-23 v1
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].
Cite
@article{arxiv.math/0703018,
title = {Poisson limits of sums of point processes and a particle-survivor model},
author = {Matthew O. Jones and Richard F. Serfozo},
journal= {arXiv preprint arXiv:math/0703018},
year = {2007}
}
Comments
Published at http://dx.doi.org/10.1214/105051606000000763 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)