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Population-size-dependent branching process with linear rate of growth

Published online by Cambridge University Press:  14 July 2016

F. C. Klebaner
F. C. Klebaner*
Affiliation:
University of Melbourne
*
∗ Postal address: Department of Statistics, Richard Berry Building, University of Melbourne, Parkville, VIC 3052, Australia.
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Abstract

The process we consider is a binary splitting, where the probability of division, , depends on the population size, 2i. We show that Zn converges to ∞ almost surely on a set of positive probability. Zn/n converges in distribution to a proper limit, diverges almost surely on converges almost surely on and there are no constants cn such that Zn/cn converges in probability to a non-degenerate limit.

Keywords

MARKOV CHAINSPOPULATION MODELSTATE DEPENDENCEGROWTH RATES
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 2 , June 1983 , pp. 242 - 250
Copyright
Copyright © Applied Probability Trust 1983 

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References

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