Transition phenomena for ladder epochs of random walks with small negative drift
Vitali Wachtel
Source: Adv. in Appl. Probab. Volume 41, Number 4
(2009), 1189-1214.
Abstract
For a family of random walks {S(a)} satisfying E S1(a)=-a<0, we consider ladder epochs τ(a)=min {k≥1: Sk (a)<0}. We study the asymptotic behaviour, as a\to0, of P (τ(a)>n) in the case when n=n(a)→∞. As a consequence, we also obtain the growth rates of the moments of τ^{(a)}.
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Permanent link to this document: http://projecteuclid.org/euclid.aap/1261669592
Digital Object Identifier: doi:10.1239/aap/1261669592
Zentralblatt MATH identifier: 05706696
Mathematical Reviews number (MathSciNet): MR2663242
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