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Sums of i.i.d. random variables and an application to the explosion criterion for markov branching processes

Published online by Cambridge University Press:  14 July 2016

H.-J. Schuh
H.-J. Schuh*
Affiliation:
University of Melbourne
*
∗Postal address: Department of Statistics, Richard Berry Building, University of Melbourne, Parkville, Vic 3052, Australia.
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Abstract

We give necessary and sufficient conditions for in terms of , where Sn is the sum of n i.i.d. random variables with values in]0, ∞[, and A ≧ 0. We use these results to give a probabilistic proof of the ‘explosion criterion' for continuous-time Markov branching processes, which is usually shown analytically.

Keywords

SUMS OF I.I.D. RANDOM VARIABLESTAIL-SIGMA-FIELDSTOPPING TIMESTRONG LAW OF LARGE NUMBERSPROBABILITY GENERATING FUNCTIONSCONTINUOUS-TIME (TIME-HOMOGENEOUS) MARKOV BRANCHING PROCESSESEXPLOSION CRITERION
Type
Research Paper
Information
Journal of Applied Probability , Volume 19 , Issue 1 , March 1982 , pp. 29 - 38
Copyright
Copyright © Applied Probability Trust 1982 

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References

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