点过程之和的泊松极限与粒子-存活者模型
概率论
2007-05-23 v1
摘要
我们给出相依点过程之和依分布收敛到泊松过程的充分条件。这推广了 Grigelionis [Theory Probab. Appl. 8 (1963) 172--182] 关于具有泊松极限的一致零点点过程之和的经典结果。包含一个粒子-存活者点过程收敛到泊松过程的应用。该结果阐明了 Durrett 与 Limic [Stochastic Process. Appl. 102 (2002) 301--309] 的物种竞争过程“令人惊讶的”泊松极限。
引用
@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}
}
备注
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)