%0 Journal Article
%T Exact asymptotics for the instant of crossing a curve boundary by an asymptotically stable random walk
%A Denis Denisov
%A Vitali Wachtel
%J Mathematics
%D 2014
%I arXiv
%X Suppose that $\{S_n,\ n\geq0\}$ is an asymptotically stable random walk. Let $g$ be a positive function and $T_g$ be the first time when $S_n$ leaves $[-g(n),\infty)$. In this paper we study asymptotic behaviour of $T_g$. We provide integral tests for function $g$ that guarantee $P(T_g>n)\sim V(g)P(T_0>n)$ where $T_0$ is the first strict descending ladder epoch of $\{S_n\}$
%U http://arxiv.org/abs/1403.5918v1