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Generalizations of the elementary renewal theorem to distributions defined by concave recurrence relations

Published online by Cambridge University Press:  14 July 2016

W. Reh
W. Reh*
Affiliation:
University of Mannheim
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Abstract

The paper examines the renewal function associated with a sequence of probability distributions, which is defined by concave recurrence relations or by an even more general procedure. The elementary renewal theorem is generalized to such sequences. The results can be used to establish renewal theorems for first death in branching processes, if only the possibly generation dependent probability generating functions converge to a limit.

Keywords

ELEMENTARY RENEWAL THEOREMFIRST DEATH IN AGE-DEPENDENT BRANCHING PROCESSESCONCAVE RECURRENCE RELATIONSSUPERCONVOLUTIVE SEQUENCES
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 3 , September 1977 , pp. 516 - 526
Copyright
Copyright © Applied Probability Trust 1977 

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References

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