Exact asymptotics for the instant of crossing a curve boundary by an asymptotically stable random walk

Denis Denisov; Vitali Wachtel

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arXiv · 1403.5918

Exact asymptotics for the instant of crossing a curve boundary by an asymptotically stable random walk

Denis Denisov·Vitali Wachtel

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Abstract

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 $\{S_n\}$

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BibTeX RIS

Denis Denisov, Vitali Wachtel. 2014-03-24. Exact asymptotics for the instant of crossing a curve boundary by an asymptotically stable random walk. https://arxiv.org/abs/1403.5918

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