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August, 1976 Uniform Tauberian Theorems and their Applications to Renewal Theory and First Passage Problems
Tze Leung Lai
Ann. Probab. 4(4): 628-643 (August, 1976). DOI: 10.1214/aop/1176996032

Abstract

In this paper, we prove an analogue of the classical renewal theorem for the case where there is no drift. Our proof depends on a uniform version of Spitzer's well-known theorem on ladder epochs and ladder variables, and we obtain this uniform result by using uniform Tauberian theorems. Some further applications of these uniform Tauberian theorems to other problems in renewal theory and first passage times are also given.

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Tze Leung Lai. "Uniform Tauberian Theorems and their Applications to Renewal Theory and First Passage Problems." Ann. Probab. 4 (4) 628 - 643, August, 1976. https://doi.org/10.1214/aop/1176996032

Information

Published: August, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0365.60095
MathSciNet: MR410966
Digital Object Identifier: 10.1214/aop/1176996032

Subjects:
Primary: 60F99
Secondary: 60K05

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 4 • August, 1976
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