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Extensions of a renewal theorem

Published online by Cambridge University Press:  24 October 2008

Walter L. Smith
Walter L. Smith
Affiliation:
University of North Carolina
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Extract

Let X1, X2, X3,… be a sequence of independent, identically distributed, absolutely continuous random variables whose first moment is μ1. Let Sk = X1 + X2 + … + Xk, and let fk(x) be the frequency function of Sk, defined as the k-fold convolution of f1(x). When f1(x) has been defined for all x, fk(x) is uniquely defined for all k, x. Write

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 51 , Issue 4 , October 1955 , pp. 629 - 638
Copyright
Copyright © Cambridge Philosophical Society 1955

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References

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