The first- and last-birth problems for a multitype age-dependent branching process
- 1 June 1976
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 8 (03) , 446-459
- https://doi.org/10.1017/s0001867800042348
Abstract
IfBnis the time of the first birth in thenth generation in a supercritical irreducible multitype Crump–Mode process then when there are people in every generationBn/nconverges to a constant; ifDnis the time of the last birth in thenth generation thenDn/nalso converges to a constant on the survival set. Analogous results hold for the extreme members of thenth generation in a branching random walk.Keywords
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- A Convexity Property in the Theory of Random Variables Defined on a Finite Markov ChainThe Annals of Mathematical Statistics, 1961