Geometric rate of growth in population-size-dependent branching processes
- 1 March 1984
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 21 (01) , 40-49
- https://doi.org/10.1017/s0021900200024359
Abstract
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.Keywords
This publication has 3 references indexed in Scilit:
- Population-size-dependent branching process with linear rate of growthJournal of Applied Probability, 1983
- Controlled Galton-Watson process and its asymptotic behaviorKodai Mathematical Journal, 1976
- A Limit Theorem for Generalized Random Branching Processes Depending on the Size of the PopulationTheory of Probability and Its Applications, 1972