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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
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.
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- Copyright © Applied Probability Trust 1976