The maximum of Brownian motion with parabolic drift

被引：13

作者：

Janson, Svante ^{[1
]}

Louchard, Guy ^{[2
]}

Martin-Lof, Anders ^{[3
]}

机构：

[1] Uppsala Univ, Dept Math, SE-75106 Uppsala, Sweden

[2] Univ Libre Bruxelles, Dept Informat, B-1050 Brussels, Belgium

[3] Stockholm Univ, Dept Math, SE-10691 Stockholm, Sweden

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2010年 / 15卷

关键词：

Brownian motion; parabolic drift; Airy functions; MEAN PATH; INTEGRALS; SIZE; TIME;

D O I：

10.1214/EJP.v15-830

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 study the maximum of a Brownian motion with a parabolic drift; this is a random variable that often occurs as a limit of the maximum of discrete processes whose expectations have a maximum at an interior point. We give new series expansions and integral formulas for the distribution and the first two moments, together with numerical values to high precision.

引用

页码：1893 / 1929

页数：37

共 50 条

[21] Range of Brownian motion with drift
Tanre, Etienne
Vallois, Pierre
JOURNAL OF THEORETICAL PROBABILITY, 2006, 19 (01) : 45 - 69
[22] Range of Brownian Motion with Drift
Etienne Tanré
Pierre Vallois
Journal of Theoretical Probability, 2006, 19 : 45 - 69
[23] ON RESOLVENT OF A BROWNIAN MOTION WITH DRIFT
KORI, T
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 1967, 19 (01) : 39 - &
[24] Brownian motion with singular drift
Bass, RF
Chen, ZQ
ANNALS OF PROBABILITY, 2003, 31 (02): : 791 - 817
[25] On the convex hull of a Brownian excursion with parabolic drift
Giraud, C
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2003, 106 (01) : 41 - 62
[26] Brownian motion on a manifold as a limit of Brownian motions with drift
P. Yu. Tarasenko
Russian Journal of Mathematical Physics, 2007, 14 : 505 - 508
[27] Brownian motion on a manifold as a limit of Brownian motions with drift
Tarasenko, P. Yu.
RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS, 2007, 14 (04) : 505 - 508
[28] Scaled Penalization of Brownian Motion with Drift and the Brownian Ascent
Panzo, Hugo
SEMINAIRE DE PROBABILITES L, 2019, 2252 : 257 - 300
[29] The first exit time of fractional Brownian motion from the minimum and maximum parabolic domains
Lu, Dawei
Zhou, Yinbing
STATISTICS & PROBABILITY LETTERS, 2022, 186
[30] On the maximum of a fractional Brownian motion
Molchan, GM
THEORY OF PROBABILITY AND ITS APPLICATIONS, 1999, 44 (01) : 97 - 102

← 1 2 3 4 5 →