A renewal theorem and supremum of a perturbed random walk

Ewa Damek , Bartosz Kołodziejek

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.
Author Ewa Damek - [University of Wroclaw]
Ewa Damek,,
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, Bartosz Kołodziejek (FMIS / DPMS)
Bartosz Kołodziejek,,
- Department of Probability and Mathematical Statistics
Journal seriesElectronic Communications in Probability, ISSN 1083-589X, (A 20 pkt)
Issue year2018
Vol23
Pages1-13
Publication size in sheets0.6
Keywords in Polishzaburzony spacer losowy; funkcje regularnie zmieniające się; teoria odnowy
Keywords in Englishperturbed random walk; regular variation; renewal theory
ASJC Classification1804 Statistics, Probability and Uncertainty; 2613 Statistics and Probability
Abstract in PolishW pracy znaleziono asymptotykę pierwszego i drugiego rzędu całek z pewnej klasy funkcji względem miary odnowy. Wynik ten został zastosowany do analizy ogonów supremum zaburzonego spaceru losowego.
DOIDOI:10.1214/18-ECP184
URL https://projecteuclid.org/euclid.ecp/1540346606
Languageen angielski
Score (nominal)20
ScoreMinisterial score = 20.0, 23-09-2019, ArticleFromJournal
Publication indicators Scopus Citations = 3; WoS Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2017 = 0.719; WoS Impact Factor: 2017 = 0.531 (2) - 2017=0.714 (5)
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