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Some applications of renewal theory on the whole line

Published online by Cambridge University Press:  14 July 2016

Kenny S. Crump  and
David G. Hoel
Kenny S. Crump
Affiliation:
Louisiana Technical University
David G. Hoel
Affiliation:
Oak Ridge National Laboratory
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Extract

Suppose F is a one-dimensional distribution function, that is, a function from the real line to the real line that is right-continuous and non-decreasing. For any such function F we shall write F{I} = F(b)– F(a) where I is the half-open interval (a, b]. Denote the k-fold convolution of F with itself by Fk* and let Now if z is a non-negative function we may form the convolution although Z may be infinite for some (and possibly all) points.

Type
Research Papers
Information
Journal of Applied Probability , Volume 7 , Issue 3 , December 1970 , pp. 734 - 746
Copyright
Copyright © Applied Probability Trust 1970 

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References

Feller, W. and Orey, S. (1961) A renewal theorem. J. Math. Mech. 10, 619–624.Google Scholar
Feller, W. (1966) An Introduction to Probability Theory and its Applications, Vol. II. Wiley, New York.Google Scholar
Harris, T. (1963) The Theory of Branching Processes. Prentice Hall, New York.Google Scholar
Kubitschek, H. E. (1962) Normal distribution of cell generation rate. Experimental Cell Research 26, 439–450.Google Scholar
Smith, W. L. (1958) Renewal theory and its ramifications. J. R. Statist. Soc. B 20, 243–302.Google Scholar