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Transition phenomena for ladder epochs of random walks with small negative drift
Published online by Cambridge University Press: 01 July 2016
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⇒0, 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).
MSC classification
- Type
- General Applied Probability
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- Copyright © Applied Probability Trust 2009