Electronic Communications in Probability

A renewal theorem and supremum of a perturbed random walk

Ewa Damek and Bartosz Kołodziejek

Full-text: Open access

Abstract

We study tails of the supremum of a perturbed random walk under regime which was not yet considered in the literature. Our approach is based on a new renewal theorem, which is of independent interest.

We obtain first and second order asymptotics of the solution to renewal equation under weak assumptions and we apply these results to obtain first and second order asymptotics of the tail of the supremum of a perturbed random walk.

Article information

Source
Electron. Commun. Probab., Volume 23 (2018), paper no. 82, 13 pp.

Dates
Received: 20 August 2018
Accepted: 15 October 2018
First available in Project Euclid: 24 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1540346606

Digital Object Identifier
doi:10.1214/18-ECP184

Mathematical Reviews number (MathSciNet)
MR3873789

Zentralblatt MATH identifier
06964425

Subjects
Primary: 60H25: Random operators and equations [See also 47B80]
Secondary: 60E99: None of the above, but in this section

Keywords
perturbed random walk regular variation renewal theory

Rights
Creative Commons Attribution 4.0 International License.

Citation

Damek, Ewa; Kołodziejek, Bartosz. A renewal theorem and supremum of a perturbed random walk. Electron. Commun. Probab. 23 (2018), paper no. 82, 13 pp. doi:10.1214/18-ECP184. https://projecteuclid.org/euclid.ecp/1540346606


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