The simple branching process with infinite mean. I
- 1 March 1973
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 10 (1) , 206-212
- https://doi.org/10.2307/3212508
Abstract
The simple branching process {Zn} with mean number of offspring per individual infinite, is considered. Conditions under which there exists a sequence {pn} of positive constants such that pn log (1 +Zn) converges in law to a proper limit distribution are given, as is a supplementary condition necessary and sufficient for pn~ constant cn as n→∞, where 0 < c < 1 is a number characteristic of the process. Some properties of the limiting distribution function are discussed; while others (with additional results) are deferred to a sequel.Keywords
This publication has 6 references indexed in Scilit:
- The Galton-Watson process with infinite meanJournal of Applied Probability, 1970
- On Koenigs' ratios for iterates of real functionsJournal of the Australian Mathematical Society, 1969
- Functional equations and the Galton-Watson processAdvances in Applied Probability, 1969
- On Recent Theorems Concerning the Supercritical Galton-Watson ProcessThe Annals of Mathematical Statistics, 1968
- Note on Schröder's functional equationJournal of the Australian Mathematical Society, 1964
- Regular iteration of real and complex functionsActa Mathematica, 1958