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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

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