Electronic Journal of Probability

Renewal theory for asymmetric $U$-statistics

Svante Janson

Full-text: Open access

Abstract

We extend a functional limit theorem for symmetric $U$-statistics [Miller and Sen, 1972] to asymmetric $U$-statistics, and use this to show some renewal theory results for asymmetric $U$-statistics.

Some applications are given.

Article information

Source
Electron. J. Probab., Volume 23 (2018), paper no. 129, 27 pp.

Dates
Received: 16 April 2018
Accepted: 27 November 2018
First available in Project Euclid: 21 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1545361593

Digital Object Identifier
doi:10.1214/18-EJP252

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60F17: Functional limit theorems; invariance principles 60K05: Renewal theory

Keywords
$U$-statistics renewal theory functional limit theorems

Rights
Creative Commons Attribution 4.0 International License.

Citation

Janson, Svante. Renewal theory for asymmetric $U$-statistics. Electron. J. Probab. 23 (2018), paper no. 129, 27 pp. doi:10.1214/18-EJP252. https://projecteuclid.org/euclid.ejp/1545361593


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