Authors
Denis Denisov, Vsevolod Shneer
Publication date
2007/3
Journal
Advances in applied probability
Volume
39
Issue
1
Pages
221-244
Publisher
Cambridge University Press
Description
Let ξ, ξ1, ξ2,… be a sequence of independent and identically distributed random variables, and let Sn=ξ1+⋯+ξn and Mn=maxk≤nSk. Let τ=min{n≥1: Sn≤0}. We assume that ξ has a heavy-tailed distribution and negative, finite mean E(ξ)<0. We find the asymptotics of P{Mτ ∈ (x, x+T]} as x→∞, for a fixed, positive constant T.
Scholar articles
D Denisov, V Shneer - Advances in applied probability, 2007