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A note on explosiveness of Markov branching processes

Published online by Cambridge University Press:  01 July 2016

D. R. Grey
D. R. Grey*
Affiliation:
University of Sheffield
*
∗Postal address: Department of Probability and Statistics, The University, Sheffield S3 7RH, UK.
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Abstract

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It is shown that no condition of the form E[g(N)] =∞, where N denotes a typical family size, is sufficient for explosiveness of a Markov branching process.

Keywords

EXPLOSION CRITERIONMOMENT CONDITION
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 21 , Issue 1 , March 1989 , pp. 226 - 228
Copyright
Copyright © Applied Probability Trust 1989 

References

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Grey, D. R. (1978) Three lemmas after Besicovitch and their applications in probability theory. J. London Math. Soc. (2) 18, 173–180.Google Scholar
Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.CrossRefGoogle Scholar