Transition phenomena for ladder epochs of random walks with small negative drift

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dc.creatorWachtel, Vitali
dc.date2009-05-08
dc.date.accessioned2026-07-07T13:13:00Z
dc.date.available2026-07-07T13:13:00Z
dc.descriptionFor a family of random walks $\{S^{(a)}\}$ satisfying $\mathbf{E}S_1^{(a)}=-a<0$ we consider ladder epochs $τ^{(a)}=\min\{k\geq1: S_k^{(a)}<0\}$. We study the asymptotic, as $a\to0$, behaviour of $\mathbf{P}(τ^{(a)}>n)$ in the case when $n=n(a)\to\infty$. As a consequence we obtain also the growth rates of the moments of $τ^{(a)}$.
dc.description27 pages
dc.identifierhttps://arxiv.org/abs/0905.1186
dc.identifierhttp://arxiv.org/abs/0905.1186
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/229755
dc.subjectProbability
dc.subject60G50; 60G52
dc.titleTransition phenomena for ladder epochs of random walks with small negative drift
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