Maximum on a random time interval of a random walk with infinite mean

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Abstract

Let ξ1,ξ2,… be independent, identically distributed random variables with infinite mean E[|ξ1|]=∞. Consider a random walk Sn=ξ1+⋯+ξn, a stopping time τ=min{n≥1:Sn≤0} and let Mτ=max0≤i≤τSi. We study the asymptotics for P(Mτ>x), as x→∞.

Bibliographical metadata

Original languageEnglish
JournalQueueing Systems
Early online date23 Jun 2020
DOIs
Publication statusE-pub ahead of print - 23 Jun 2020