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Conditional limit theorems for general branching processes

Published online by Cambridge University Press:  14 July 2016

P. J. Green
P. J. Green*
Affiliation:
University of Bath
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Abstract

In this paper we generalise the so-called Yaglom conditional limit theorems to the general branching process counted by the values of a random characteristic, as suggested by Jagers (1974). Even when restricted to the special case of the usual population-size process, our results are stronger than those previously available.

Keywords

CONDITIONAL LIMIT THEOREMSGENERAL BRANCHING PROCESSRANDOM CHARACTERISTIC
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 3 , September 1977 , pp. 451 - 463
Copyright
Copyright © Applied Probability Trust 1977 

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References

Athreya, K. B. and Ney, P. E. (1972) Branching Processes. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Crump, K. S. and Mode, C. J. (1968), (1969) A general age-dependent branching process, I and II. J. Math. Anal. Appl. 24, 494–508 and 25, 8–17.CrossRefGoogle Scholar
Durham, S. D. (1971) Limit theorems for a general critical branching process. J. Appl. Prob. 8, 1–16.CrossRefGoogle Scholar
Goldstein, ?. I. (1971) Critical age-dependent branching processes: single and multitype. Z. Wahrscheinlichkeitsch. 17, 74–88.CrossRefGoogle Scholar
Green, P. J. (1976) Random Variables on Branching Process Paths. Ph.D. Thesis, University of Sheffield.Google Scholar
Green, P. J. (1977) Conditioning a branching process on non-extinction. Math. Biosci 34. To appear.Google Scholar
Holte, J. M. (1974) Extinction probability for a critical general branching process. Stoch. Proc. Appl. 2, 303–309.CrossRefGoogle Scholar
Holte, J. ?. (1976) A generalization of Goldstein's comparison lemma and the exponential limit law in critical Crump–Mode–Jagers branching processes. Adv. Appl. Prob. 8, 88–104.CrossRefGoogle Scholar
Jagers, P. (1969) A general stochastic model for population development. Skand. Ak-tuarietidskr. 52, 84–103.Google Scholar
Jagers, P. (1974) Convergence of general branching processes and functionals thereof. J. Appl. Prob. 11, 471–478.CrossRefGoogle Scholar
Jagers, P. (1975) Branching Processes with Biological Applications. Wiley, New York.Google Scholar
Ryan, T. A. (1968) On Age-Dependent Branching Processes. Ph.D. Thesis, Cornell University.Google Scholar