2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229755For 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 $τ^{(a)}$.27 pagesProbability60G50; 60G52text