Bounds for the Asymptotic Growth Rate of an Age-Dependent Branching Process
- 1 August 1969
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 10 (1-2), 231-235
- https://doi.org/10.1017/s1446788700007114
Abstract
Let M(t) denote the mean population size at time t (conditional on a single ancestor of age zero at time zero) of a branching process in which the distribution of the lifetime T of an individual is given by Pr {T≦t} =G(t), and in which each individual gives rise (at death) to an expected number A of offspring (1λ A λ ∞). expected number A of offspring (1 < A ∞). Then it is well-known (Harris [1], p. 143) that, provided G(O+)-G(O-) 0 and G is not a lattice distribution, M(t) is given asymptotically by where c is the unique positive value of p satisfying the equation .Keywords
This publication has 4 references indexed in Scilit:
- On the transient behaviour of a Poisson branching processJournal of the Australian Mathematical Society, 1967
- Bounds for moment generating functions and for extinction probabilitiesJournal of Applied Probability, 1966
- Inequalities for branching processesJournal of Applied Probability, 1966
- The Theory of Branching ProcessesPublished by Springer Nature ,1963