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A note on some results of Schuh

Published online by Cambridge University Press:  14 July 2016

R. A. Doney
R. A. Doney*
Affiliation:
The University of Manchester
*
∗ Postal address: Statistical Laboratory, Department of Mathematics, The University, Manchester M13 9PL, U.K.
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Abstract

We extend recent results of Schuh on the convergence of , where α ≧ 0 and Sn is the sum of n i.i.d. positive random variables to sums of the form for a large class of functions g, give simpler proofs than those of Schuh, and derive reformulations of the explosion criteria for Markov branching processes with discrete and continuous state space.

Keywords

SUMS OF I.I.D. RANDOM VARIABLESRENEWAL THEORYMARKOV BRANCHING PROCESSCONTINUOUS BRANCHING PROCESSEXPLOSION CRITERION
Type
Short Communications
Information
Journal of Applied Probability , Volume 21 , Issue 1 , March 1984 , pp. 192 - 196
Copyright
Copyright © Applied Probability Trust 1984 

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References

[1] Bingham, N. H. (1976) Continuous branching processes and spectral positivity. Stoch. Proc. Appl. 4, 217–242.CrossRefGoogle Scholar
[2] Erickson, K. B. (1973) The strong law of large numbers when the mean is undefined. Trans. Amer. Math. Soc. 85, 371–381.CrossRefGoogle Scholar
[3] Gihman, I. I. and Skorohod, A. V. (1975) The Theory of Stochastic Processes, Vol. II. Springer-Verlag, Berlin.Google Scholar
[4] Grey, D. R. (1974) Asymptotic behaviour of continuous state-space branching processes. J. Appl. Prob. 11, 669–677.CrossRefGoogle Scholar
[5] Lamperti, J. (1967) Continuous-state branching processes. Bull. Amer. Math. Soc. 73, 382–386.CrossRefGoogle Scholar
[6] Schuh, H.-J. (1982) Sums of i.i.d. random variables and an application to the explosion criterion for Markov branching processes. J. Appl. Prob. 19, 29–38.CrossRefGoogle Scholar