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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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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

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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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