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

Matthew O. Jones·Richard F. Serfozo
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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].

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Matthew O. Jones, Richard F. Serfozo. 2007-03-01. Poisson limits of sums of point processes and a particle-survivor model. https://doi.org/10.1214/105051606000000763

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