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Remarks on the maxima of a martingale sequence with application to the simple critical branching process

Published online by Cambridge University Press:  14 July 2016

Anthony G. Pakes
Anthony G. Pakes*
Affiliation:
University of Western Australia
*
∗Postal address: Department of Mathematics, University of Western Australia, Nedlands, WA 6009, Australia.
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Abstract

Let where {Zn, ℱn} is a non-negative submartingale satisfying Ei(Zn log Zn) →∞. It is shown that When {Zn} is a simple critical Galton–Watson process and is slowly varying at∞, conditions are given ensuring that This gives an alternative proof of a result recently established by Kammerle and Schuh.

Keywords

MARTINGALE INEQUALITIES
Type
Short Communications
Information
Journal of Applied Probability , Volume 24 , Issue 3 , September 1987 , pp. 768 - 772
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

Research carried out while the author was visiting Colorado State University, Fort Collins.

References

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