Electronic Communications in Probability

A renewal theorem and supremum of a perturbed random walk

Ewa Damek and Bartosz Kołodziejek

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

perturbed random walk regular variation renewal theory

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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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