Translator Disclaimer
2018 A renewal theorem and supremum of a perturbed random walk
Ewa Damek, Bartosz Kołodziejek
Electron. Commun. Probab. 23: 1-13 (2018). DOI: 10.1214/18-ECP184

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.

Citation

Download Citation

Ewa Damek. Bartosz Kołodziejek. "A renewal theorem and supremum of a perturbed random walk." Electron. Commun. Probab. 23 1 - 13, 2018. https://doi.org/10.1214/18-ECP184

Information

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

zbMATH: 06964425
MathSciNet: MR3873789
Digital Object Identifier: 10.1214/18-ECP184

Subjects:
Primary: 60H25
Secondary: 60E99

JOURNAL ARTICLE
13 PAGES


SHARE
Back to Top