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A class of infinitely divisible random variables

Published online by Cambridge University Press:  24 October 2008

Charles Goldie
Charles Goldie
Affiliation:
Statistical Laboratory, Cambridge
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Extract

The question has arisen in the theory of queues whether the product of two independent exponentially distributed random variables is infinitely divisible. In this note it is proved that the product of any non-negative random variable with an independent exponentially distributed variable is infinitely divisible. Such random variables are members of a wider class of infinitely divisible random variables, which will be exhibited first.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 4 , October 1967 , pp. 1141 - 1143
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Feller, W.An introduction to probability theory and its applications, vol. 2 (Wiley, 1966).Google Scholar
(2)Kaluza, Th.Über die Koeffizienten reziproker Potenzreihen. Math. Z. 28 (1928), 161–170.CrossRefGoogle Scholar
(3)Lamperti, J.On the coefficients of reciprocal power series. Amer. Math. Monthly 65 (1958), 90–94.CrossRefGoogle Scholar
(4)Keilson, J. and Runnenberg, J. Th. Discussion to Ch. 6 of Smith, W. L. and Wilkinson, W. E. (ed.). Proceedings of the Symposium on Congestion Theory (Chapel Hill, 1966).Google Scholar
(5)Kingman, J. F. C.On queues in which customers are served in random order. Proc. Cambridge Philos. Soc. 58 (1962), 79–91.CrossRefGoogle Scholar
(6)Kingman, J. F. C.An approach to the study of Markov processes. J. Roy. Statist. Soc. Ser. B 28 (1966), 417–447.Google Scholar
(7)Le Gall, P. Les systemes avec ou sans attente et les processus stochastiques, tom. 1 (Dunod, 1962).Google Scholar