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Malthusian behaviour of the critical and subcritical age-dependent branching processes with arbitrary state space

Published online by Cambridge University Press:  14 July 2016

D. I. Saunders
D. I. Saunders*
Affiliation:
South Australian Institute of Technology, Ingle Farm, South Australia
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Abstract

For the age-dependent branching process with arbitrary state space let M(x, t, A) be the expected number of individuals alive at time t with states in A given an initial individual at x. Subject to various conditions it is shown that M(x, t, A)e–at converges to a non-trivial limit where α is the Malthusian parameter (α = 0 for the critical case, and is negative in the subcritical case). The method of proof also yields rates of convergence.

Keywords

AGE-DEPENDENTBRANCHING PROCESSARBITRARY STATE SPACEMALTHUSIAN BEHAVIOUR
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 3 , September 1976 , pp. 455 - 465
Copyright
Copyright © Applied Probability Trust 1976 

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