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First-passage times over moving boundaries for asymptotically stable walks. / Denisov, D.; Sakhanenko, A.; Wachtel, V.

In: Theory of Probability and its Applications, Vol. 63, No. 4, 01.01.2019, p. 613-633.

Research output: Contribution to journal › Article › peer-review

Harvard

Denisov, D, Sakhanenko, A & Wachtel, V 2019, 'First-passage times over moving boundaries for asymptotically stable walks', Theory of Probability and its Applications, vol. 63, no. 4, pp. 613-633. https://doi.org/10.1137/S0040585X97T989283

APA

Denisov, D., Sakhanenko, A., & Wachtel, V. (2019). First-passage times over moving boundaries for asymptotically stable walks. Theory of Probability and its Applications, 63(4), 613-633. https://doi.org/10.1137/S0040585X97T989283

Vancouver

Denisov D, Sakhanenko A, Wachtel V. First-passage times over moving boundaries for asymptotically stable walks. Theory of Probability and its Applications. 2019 Jan 1;63(4):613-633. doi: 10.1137/S0040585X97T989283

Author

Denisov, D. ; Sakhanenko, A. ; Wachtel, V. / First-passage times over moving boundaries for asymptotically stable walks. In: Theory of Probability and its Applications. 2019 ; Vol. 63, No. 4. pp. 613-633.

BibTeX

@article{1617abc8e4c74e589ec376ea4a34d439,
title = "First-passage times over moving boundaries for asymptotically stable walks",
abstract = " 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. ",
keywords = "First-passage time, Moving boundary, Overshoot, Random walk, Stable distribution, random walk, overshoot, first-passage time, stable distribution, moving boundary",
author = "D. Denisov and A. Sakhanenko and V. Wachtel",
year = "2019",
month = jan,
day = "1",
doi = "10.1137/S0040585X97T989283",
language = "English",
volume = "63",
pages = "613--633",
journal = "Theory of Probability and its Applications",
issn = "0040-585X",
publisher = "SIAM PUBLICATIONS",
number = "4",

}

RIS

TY - JOUR

T1 - First-passage times over moving boundaries for asymptotically stable walks

AU - Denisov, D.

AU - Sakhanenko, A.

AU - Wachtel, V.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - First-passage time

KW - Moving boundary

KW - Overshoot

KW - Random walk

KW - Stable distribution

KW - random walk

KW - overshoot

KW - first-passage time

KW - stable distribution

KW - moving boundary

UR - http://www.scopus.com/inward/record.url?scp=85064669423&partnerID=8YFLogxK

U2 - 10.1137/S0040585X97T989283

DO - 10.1137/S0040585X97T989283

M3 - Article

AN - SCOPUS:85064669423

VL - 63

SP - 613

EP - 633

JO - Theory of Probability and its Applications

JF - Theory of Probability and its Applications

SN - 0040-585X

IS - 4

ER -

ID: 19630170