Boundary non-crossing probabilities for fractional Brownian motion with trend

被引：5
作者：
Hashorva, Enkelejd [1 ]
Mishura, Yuliya [2 ]
Seleznjev, Oleg [3 ]
机构：
[1] Univ Lausanne, Dept Actuarial Sci, UNIL Dorigny, CH-1015 Lausanne, Switzerland
[2] Taras Shevchenko Natl Univ Kyiv, Dept Probabil Stat & Actuarial Math, UA-01601 Kiev, Ukraine
[3] Umea Univ, Dept Math & Math Stat, SE-90187 Umea, Sweden
来源：
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES | 2015年 / 87卷 / 06期
关键词：
boundary crossings; Cameron-Martin-Girsanov theorem; reproducing kernel Hilbert space; large deviation principle; Molchan martingale; fractional Brownian motion; EXACT ASYMPTOTICS; BRIDGE; POWER;
D O I：
10.1080/17442508.2015.1019882
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate the boundary non-crossing probabilities of a fractional Brownian motion considering some general deterministic trend function. We derive bounds for non-crossing probabilities and discuss the case of a large trend function. As a by-product, we solve a minimization problem related to the norm of the trend function.
引用
收藏
页码：946 / 965
页数：20
相关论文
共 32 条
[1]   Boundary-Crossing Identities for Diffusions Having the Time-Inversion Property [J].
Alili, L. ;
Patie, P. .
JOURNAL OF THEORETICAL PROBABILITY, 2010, 23 (01) :65-84
[2]  
Biagini F, 2008, PROBAB APPL SER, P1
[3]   A lower bound for boundary crossing probabilities of Brownian bridge/motion with trend [J].
Bischoff, W ;
Hashorva, E .
STATISTICS & PROBABILITY LETTERS, 2005, 74 (03) :265-271
[4]   Analysis of a change-point regression problem in quality control by partial sums processes and Kolmogorov type tests [J].
Bischoff, W ;
Hashorva, E ;
Hüsler, J ;
Miller, F .
METRIKA, 2005, 62 (01) :85-98
[5]   On the power of the Kolmogorov test to detect the trend of a Brownian bridge with applications to a change-point problem in regression models [J].
Bischoff, W ;
Hashorva, E ;
Hüsler, K ;
Miller, F .
STATISTICS & PROBABILITY LETTERS, 2004, 66 (02) :105-115
[6]   Asymptotics of a boundary crossing probability of a Brownian bridge with general trend [J].
Bischoff, W ;
Miller, F ;
Hashorva, E ;
Hüsler, J .
METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 2003, 5 (03) :271-287
[7]   Exact asymptotics for boundary crossings of the Brownian bridge with trend with application to the Kolmogorov test [J].
Bischoff, W ;
Hashorva, E ;
Hüsler, J ;
Miller, F .
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 2003, 55 (04) :849-864
[8]   An asymptotic result for non crossing probabilities of brownian motion with trend [J].
Bischoff, Wolfgang ;
Hashorva, Enkelejd ;
Huesler, Juerg .
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2007, 36 (13-16) :2821-2828
[9]   The Cameron-Martin Theorem for (p-)Slepian Processes [J].
Bischoff, Wolfgang ;
Gegg, Andreas .
JOURNAL OF THEORETICAL PROBABILITY, 2016, 29 (02) :707-715
[10]   Explicit bounds for approximation rates of boundary crossing probabilities for the Wiener process [J].
Borovkov, K ;
Novikov, A .
JOURNAL OF APPLIED PROBABILITY, 2005, 42 (01) :82-92
1234