Аннотация
Let {S n ,n≥ 1} be a random walk with independent and identically distributed increments, and let {g n ,n≥ 1} be a sequence of real numbers. Let T g denote the first time when S n leaves (g n , ∞). Assume that the random walk is oscillating and asymptotically stable, that is, there exists a sequence {c n ,n≥ 1} such that S n /c n converges to a stable law. In this paper we determine the tail behavior of T g for all oscillating asymptotically stable walks and all boundary sequences satisfying g n = o(c n ). Furthermore, we prove that the rescaled random walk conditioned to stay above the boundary up to time n converges, as n →∞, towards the stable meander.
Язык оригинала | английский |
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Страницы (с-по) | 613-633 |
Число страниц | 21 |
Журнал | Theory of Probability and its Applications |
Том | 63 |
Номер выпуска | 4 |
DOI | |
Состояние | Опубликовано - 1 янв 2019 |