The Annals of Probability

Uniform Tauberian Theorems and their Applications to Renewal Theory and First Passage Problems

Tze Leung Lai

Full-text: Open access

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.

Article information

Source
Ann. Probab., Volume 4, Number 4 (1976), 628-643.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996032

Digital Object Identifier
doi:10.1214/aop/1176996032

Mathematical Reviews number (MathSciNet)
MR410966

Zentralblatt MATH identifier
0365.60095

JSTOR
links.jstor.org

Subjects
Primary: 60F99: None of the above, but in this section
Secondary: 60K05: Renewal theory

Keywords
Renewal theory first passage problems ladder epoch ladder variable uniform Tauberian theorems uniform strong law of large numbers Paley-type inequalities

Citation

Lai, Tze Leung. Uniform Tauberian Theorems and their Applications to Renewal Theory and First Passage Problems. Ann. Probab. 4 (1976), no. 4, 628--643. doi:10.1214/aop/1176996032. https://projecteuclid.org/euclid.aop/1176996032


Export citation