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Convergence of weighted sums of independent random variables

Published online by Cambridge University Press:  24 October 2008

V. K. Rohatgi
V. K. Rohatgi
Affiliation:
The Catholic University of America, Washington, D.C.
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Extract

1. Introduction. Let {Xk: k ≥ 1} be a sequence of independent, but not necessarily identically distributed, random variables. Suppose that the random variables Xn are uniformly bounded by a random variable X in the sense that

(1) P(|Xn| ≥x) ≤ P(|X| ≥ x)for all x > 0. Write qn(x) = P(|Xn| ≥ x) and q(x) = P(|X| ≥ x).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 69 , Issue 2 , March 1971 , pp. 305 - 307
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

REFERENCE

(1) Pruitt, W. E.Summability of independent random variables. J. Math. Mech. 15 (1966), 769–776.Google Scholar