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

  • F. C. Klebaner (a1)


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.


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Postal address: Department of Statistics, Richard Berry Building, University of Melbourne, Parkville, VIC 3052, Australia.


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