Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poisson limits of sums of point processes and a particle-survivor model   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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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: hep-th