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The xlogx condition for general branching processes

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Peter Olofsson
Peter Olofsson*
Affiliation:
Rice University
*
∗Postal address: Department of Statistics – MS 138, Rice University, 6100 Main Street, Houston, TX 77005–1892, USA. Email address: olofsson@stat.rice.edu.
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Abstract

The xlogx condition is a fundamental criterion for the rate of growth of a general branching process, being equivalent to non-degeneracy of the limiting random variable. In this paper we adopt the ideas from Lyons, Pemantle and Peres (1995) to present a new proof of this well-known theorem. The idea is to compare the ordinary branching measure on the space of population trees with another measure, the size-biased measure.

Keywords

General branching processx log x conditionimmigration

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 3 , September 1998 , pp. 537 - 544
Copyright
Copyright © Applied Probability Trust 1998 

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References

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