Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-12-07T05:48:48.346Z Has data issue: false hasContentIssue false

Some divisibility problems in branching processes

Published online by Cambridge University Press:  24 October 2008

J. D. Biggins
Affiliation:
University of Sheffield
D. N. Shanbhag
Affiliation:
University of Sheffield

Extract

In this paper the major concern is in investigating various divisibility properties of the random variable W, the limit of the Heyde martingale in supercritical branching processes. Throughout the paper ø(s) will be used to denote the Laplace-Stieltjes transform of W.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1981

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Asmussen, S. Some martingale methods in the limit theory of supercritical branching processes. Advances in Probability and Related Topics, ed. Joffe, A. and Ney, P., 5, 126.Google Scholar
(2)Athreya, K. B.A note on a functional equation arising in Galton-Watson branching processes. J. Appl. Prob. 8 (1971), 589598.CrossRefGoogle Scholar
(3)Athreya, K. B. and Ney, P. E.Branching processes (Springer, Berlin, 1972).CrossRefGoogle Scholar
(4)Bingham, N. H. and Doney, R. A.Asymptotic properties of supercritical branching processes. I. The Galton-Watson case. Adv. Appl. Prob. 6 (1974), 711731.CrossRefGoogle Scholar
(5)Bingham, N. H.Continuous branching processes and spectral positivity. Stock. Proc. & Appl. 4 (1975), 217242.CrossRefGoogle Scholar
(6)Feller, W.An introduction to probability theory and its applications (John Wiley, New York, 1971).Google Scholar
(7)Harris, T. E.Branching processes. Ann. Math. Statist 19 (1948), 474494.CrossRefGoogle Scholar
(8)Harris, T. E.Some mathematical models for branching processes. 2nd Berk. Symp. 305328.Google Scholar
(9)Lukacs, E.Characteristic functions, 2nd ed. (Griffin, London, 1970).Google Scholar
(10)Prabhu, N. U.Queues and inventories: a study of their basic stochastic processes (John Wiley, New York, 1965).Google Scholar
(11)Prabhu, N. U.Stochastic processes (Macmillan, New York, 1965).Google Scholar
(12)Titchmarsh, E. C.The theory of functions (Macmillan, New York, 1965).Google Scholar