ON THE ONE-SIDED EXIT PROBLEM FOR FRACTIONAL BROWNIAN MOTION

被引：25

作者：

Aurzada, Frank ^{[1
]}

机构：

[1] Tech Univ Berlin, D-1000 Berlin, Germany

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2011年 / 16卷

关键词：

First passage time; fractional Brownian motion; lower tail probability; one-sided barrier problem; one-sided exit problem; small value probability; survival exponent; INVISCID BURGERS-EQUATION; PROBABILITIES;

D O I：

10.1214/ECP.v16-1640

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider the one-sided exit problem for fractional Brownian motion (FBM), which is equivalent to the question of the distribution of the lower tail of the maximum of FBM on the unit interval. We improve the bounds given by Molchan (1999) and shed some light on the relation to the quantity I studied there.

引用

页码：392 / 404

页数：13

共 50 条

[21] ON THE ONE-SIDED WIENER THEOREM FOR THE MOTION GROUP
WEIT, Y
[J]. ANNALS OF MATHEMATICS, 1980, 111 (03) : 415 - 422
[22] One-sided reflected Brownian motions and the KPZ fixed point
Nica, Mihai
Quastel, Jeremy
Remenik, Daniel
[J]. FORUM OF MATHEMATICS SIGMA, 2020, 8
[23] Limit theorems for a diffusion process with a one-sided Brownian potential
Kawazu, Kiyoshi
Suzuki, Yuki
[J]. JOURNAL OF APPLIED PROBABILITY, 2006, 43 (04) : 997 - 1012
[24] Weights for commutators of the one-sided discrete square function, the Weyl fractional integral and other one-sided operators
Lorente, M
Riveros, MS
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2005, 135 : 845 - 862
[25] Regularity of one-sided multilinear fractional maximal functions
Liu, Feng
Xu, Lei
[J]. OPEN MATHEMATICS, 2018, 16 : 1556 - 1572
[26] Weighted inequalities for one-sided fractional minimal function
Chutia, Duranta
Haloi, Rajib
[J]. JOURNAL OF ANALYSIS, 2021, 29 (04): : 1151 - 1163
[27] Weighted inequalities for one-sided multilinear fractional integrals
Imerlishvili, Giorgi
Meskhi, Alexander
[J]. POSITIVITY, 2023, 27 (01)
[28] Weighted inequalities for one-sided fractional minimal function
Duranta Chutia
Rajib Haloi
[J]. The Journal of Analysis, 2021, 29 : 1151 - 1163
[29] Weighted inequalities for one-sided multilinear fractional integrals
Giorgi Imerlishvili
Alexander Meskhi
[J]. Positivity, 2023, 27
[30] One-sided fractional derivatives, fractional Laplacians, and weighted Sobolev spaces
Stinga, Pablo Raul
Vaughan, Mary
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2020, 193

← 1 2 3 4 5 →