The Annals of Probability

Invariance Principles for Renewal Processes

Miklos Csorgo, Lajos Horvath, and Josef Steinebach

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Abstract

We present a general methodology for proving invariance principles for renewal processes, resulting in almost sure and probability inequality approximations. We show that our obtained rates are best possible in the i.i.d. case.

Article information

Source
Ann. Probab., Volume 15, Number 4 (1987), 1441-1460.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991986

Digital Object Identifier
doi:10.1214/aop/1176991986

Mathematical Reviews number (MathSciNet)
MR905341

Zentralblatt MATH identifier
0635.60032

JSTOR
links.jstor.org

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60K05: Renewal theory

Keywords
Renewal process Wiener process strong approximation probability inequalities Prohorov-Levy distance

Citation

Csorgo, Miklos; Horvath, Lajos; Steinebach, Josef. Invariance Principles for Renewal Processes. Ann. Probab. 15 (1987), no. 4, 1441--1460. doi:10.1214/aop/1176991986. https://projecteuclid.org/euclid.aop/1176991986


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