Poisson limits of sums of point processes and a particle-survivor model

• 成果类型: Article
• 署名作者: Jones, Matthew O.; Serfozo, Richard F.
• 署名单位: Austin Peay State University; University System of Georgia; Georgia Institute of Technology
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051606000000763
• 发表日期: 2007
• 页码: 265-283
• 关键词: competition

摘要

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.