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Geometric rate of growth in population-size-dependent branching processes

  • F. C. Klebaner (a1)


We consider a branching-process model {Zn }, where the law of offspring distribution depends on the population size. We consider the case when the means mn (mn is the mean of offspring distribution when the population size is equal to n) tend to a limit m > 1 as n →∞. For a certain class of processes {Zn } necessary conditions for convergence in L 1 and L 2 and sufficient conditions for almost sure convergence and convergence in L 2 of Wn = Zn/mn are given.


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


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