Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 23 (2018), paper no. 82, 13 pp.
A renewal theorem and supremum of a perturbed random walk
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.
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
Permanent link to this document
Digital Object Identifier
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
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