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

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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].
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)

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Probability

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http://salesiana.dossiersoluciones.com/handle/123456789/124899

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0703018
 http://arxiv.org/abs/math/0703018
 Annals of Applied Probability 2007, Vol. 17, No. 1, 265-283
 doi:10.1214/105051606000000763

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