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Some Blackwell-Type Renewal Theorems for Weighted Renewal Functions

Part of: Distribution theory - Probability Special processes Real functions

Published online by Cambridge University Press:  14 July 2016

Jianxi Lin
Jianxi Lin*
Affiliation:
Xiamen University
*
∗Postal address: Mathematics School, Xiamen University, Xiamen, Fujian, 361005, P. R. China. Email address: linjx999@gmail.com
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Abstract

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In this paper, a new approach is proposed to investigate Blackwell-type renewal theorems for weighted renewal functions systematically according to which of the tails of weighted renewal constants or the underlying distribution is asymptotically heavier. Some classical results are improved considerably.

Keywords

Weighted renewal functionrenewal theoryBlackwell's theoremregular oscillation

MSC classification

Secondary: 60K05: Renewal theory 60E05: Distributions 26A12: Rate of growth of functions, orders of infinity, slowly varying functions
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 4 , December 2008 , pp. 972 - 993
Copyright
Copyright © Applied Probability Trust 2008 

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