Hostname: page-component-6bb9c88b65-6vlrh Total loading time: 0 Render date: 2025-07-26T04:29:47.029Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

(1) Blackwell, D. Duke math. J. 15 (1948), 145–50.Google Scholar
(2) Blackwell, D. Pacif. J. Math. 3 (1953), 315–20.Google Scholar
(3) Bochner, S. and Chandrasekharan, K. Fourier transforms (Ann. Math. Stud. no. 19, Princeton, 1949).Google Scholar
(4) Chung, K. L. and Fuchs, W. H. J. Four papers on probability (Mem. Amer. math. Soc. no. 6, 1951).Google Scholar
(5) Cox, D. R. and Smith, W. L. Skand. AktuarTidskr. (1953), pp. 139–50.Google Scholar
(6) Smith, W. L. Proc. roy. Soc. Edinb. A, 64 (1954), 9–48.Google Scholar
(7) Titchmarsh, E. C. Theory of functions, 2nd ed. (Oxford, 1939), pp. 386–8.Google Scholar