Exit times for integrated random walks

Denis Denisov; Vitali Wachtel

doi:10.1214/13-AIHP577

Exit times for integrated random walks

Denis Denisov, Vitali Wachtel

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

58 Downloads (Pure)

Abstract

We consider a centered random walk with finite variance and investigate the asymptotic behaviour of the probability that the area under this walk remains positive up to a large time n. Assuming that the moment of order 2+δ is finite, we show that the exact asymptotics for this probability is n−1/4. To show this asymptotics we develop a discrete potential theory for integrated random walks.

Original language	English
Pages (from-to)	167-193
Number of pages	26
Journal	l'Institut Henri Poincare. Annales (B). Probabilites et Statistiques
Volume	51
Issue number	1
DOIs	https://doi.org/10.1214/13-AIHP577
Publication status	Published - 14 Jan 2015

Access to Document

10.1214/13-AIHP577

PRE-PEER-REVIEW.PDFSubmitted manuscript, 367 KB

Cite this

@article{a86f4bdca523415ab456acc1108b9fe6,

title = "Exit times for integrated random walks",

abstract = "We consider a centered random walk with finite variance and investigate the asymptotic behaviour of the probability that the area under this walk remains positive up to a large time n. Assuming that the moment of order 2+δ is finite, we show that the exact asymptotics for this probability is n−1/4. To show this asymptotics we develop a discrete potential theory for integrated random walks.",

author = "Denis Denisov and Vitali Wachtel",

year = "2015",

month = jan,

day = "14",

doi = "10.1214/13-AIHP577",

language = "English",

volume = "51",

pages = "167--193",

journal = "l'Institut Henri Poincare. Annales (B). Probabilites et Statistiques",

issn = "0246-0203",

publisher = "Institute of Mathematical Statistics",

number = "1",

}

TY - JOUR

T1 - Exit times for integrated random walks

AU - Denisov, Denis

AU - Wachtel, Vitali

PY - 2015/1/14

Y1 - 2015/1/14

N2 - We consider a centered random walk with finite variance and investigate the asymptotic behaviour of the probability that the area under this walk remains positive up to a large time n. Assuming that the moment of order 2+δ is finite, we show that the exact asymptotics for this probability is n−1/4. To show this asymptotics we develop a discrete potential theory for integrated random walks.

AB - We consider a centered random walk with finite variance and investigate the asymptotic behaviour of the probability that the area under this walk remains positive up to a large time n. Assuming that the moment of order 2+δ is finite, we show that the exact asymptotics for this probability is n−1/4. To show this asymptotics we develop a discrete potential theory for integrated random walks.

U2 - 10.1214/13-AIHP577

DO - 10.1214/13-AIHP577

M3 - Article

SN - 0246-0203

VL - 51

SP - 167

EP - 193

JO - l'Institut Henri Poincare. Annales (B). Probabilites et Statistiques

JF - l'Institut Henri Poincare. Annales (B). Probabilites et Statistiques

IS - 1

ER -

Exit times for integrated random walks

Abstract

Access to Document

Fingerprint

Cite this