Article contents
A generalization of Goldstein's comparison lemma and the exponential limit law in critical Crump-Mode-Jagers branching processes
Published online by Cambridge University Press: 01 July 2016
Abstract
Let Z(t) be the population size at time t in a general age-dependent branching process (as defined by Crump and Mode, or Jagers) in which the number N of offspring of a parent has expected value 1 (critical case). Assuming positivity and finiteness of the second moments of N, of the lifespan distribution and of the expected number of births per parent as a function of age (also assumed to be strongly non-lattice), the distribution of Z(t)/t conditioned on non-extinction at time t is asymptotically exponential. The main step in the proof is a comparison lemma for the probability generating functions of Z(t) and of the embedded generation process.
- Type
- Research Article
- Information
- Copyright
- Copyright © Applied Probability Trust 1976
References
- 6
- Cited by