Population-size-dependent branching process with linear rate of growth
- 1 June 1983
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 20 (2) , 242-250
- https://doi.org/10.2307/3213798
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
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