Asymptotic properties of super-critical branching processes II: Crump-Mode and Jirina processes
- 1 March 1975
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 7 (01) , 66-82
- https://doi.org/10.1017/s0001867800040301
Abstract
We obtain results connecting the distribution of the random variablesYandWin the supercritical generalized branching processes introduced by Crump and Mode. For example, if β > 1,EYβandEWβconverge or diverge together and regular variation of the tail of one ofY, Wwith non-integer exponent β > 1 is equivalent to regular variation of the other. We also prove analogous results for the continuous-time continuous state-space branching processes introduced by Jirina.Keywords
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