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Limit theorems for point processes generated in a general branching process

Published online by Cambridge University Press:  01 July 2016

Martin Härnqvist
Martin Härnqvist*
Affiliation:
University of Göteborg
*
∗Postal address: Volvo-Data, Department of Applied Statistics, S-405 08, Göteborg, Sweden.
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Abstract

With the general convergence theory for branching processes as basis a special problem is studied. An extra point process of events during life is assigned to each realised individual, and the behaviour of the superposition of such point processes in action is studied as the population grows. With the proper scaling and under some regularity conditions the superposition is shown to converge in distribution to a Poisson process. Another scaling gives rise to a mixed Poisson process as limit.

Established weak convergence techniques for point processes are applied, together with some recent strong convergence results for branching processes.

Keywords

BRANCHING PROCESSSUPERCRITICALPOINT PROCESSSUPERPOSITIONSPOISSON PROCESS
Type
Research Article
Information
Advances in Applied Probability , Volume 13 , Issue 4 , December 1981 , pp. 650 - 668
Copyright
Copyright © Applied Probability Trust 1981 

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