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Rarefactions of compound point processes

Published online by Cambridge University Press:  14 July 2016

Richard F. Serfozo
Richard F. Serfozo*
Affiliation:
AT & T Bell Laboratories
*
∗Present address: School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA.
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Abstract

The Poisson process is regarded as a point process of rare events because of the classical result that the number of successes in a sequence of Bernoulli trials is asymptotically Poisson as the probability of a success tends to 0. It is shown that this rareness property of the Poisson process is characteristic of any infinitely divisible point process or random measure with independent increments. These processes and measures arise as limits of certain rarefactions of compound point processes: purely atomic random measures with uniformly null atom sizes. Examples include thinnings and partitions of point processes.

Keywords

POISSON PROCESSESCOX PROCESSESRANDOM MEASURESINFINITE DIVISIBILITYTHINNING OF POINT PROCESSES
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 4 , December 1984 , pp. 710 - 719
Copyright
Copyright © Applied Probability Trust 1984 

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