New and refined bounds for expected maxima of fractional Brownian motion

被引：9

作者：

Borovkov, Konstantin ^{[1
]}

Mishura, Yuliya ^{[2
]}

Novikov, Alexander ^{[3
]}

Zhitlukhin, Mikhail ^{[4
]}

机构：

[1] Univ Melbourne, Sch Math & Stat, Parkville, Vic 3010, Australia

[2] Taras Shevchenko Natl Univ Kyiv, Mech & Math Fac, Volodymyrska Str 64, UA-01601 Kiev, Ukraine

[3] Univ Technol Sydney, Sch Math & Phys Sci, POB 123, Sydney, NSW 2007, Australia

[4] Russian Acad Sci, Steklov Math Inst, Gubkina Str 8, Moscow 119991, Russia

来源：

STATISTICS & PROBABILITY LETTERS | 2018年 / 137卷

基金：

俄罗斯科学基金会;

关键词：

Fractional Brownian motion; Convergence rate; Discrete time approximation; Pickands' constant; ESTIMATORS;

D O I：

10.1016/j.spl.2018.01.025

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：

For the fractional Brownian motion B-H with the Hurst parameter value H in (0, 1/2), we derive new upper and lower bounds for the difference between the expectations of the maximum of BH over [0, 1] and the maximum of B-H over the discrete set of values in(-1), i = 1, ... , n. We use these results to improve our earlier upper bounds for the expectation of the maximum of B-H over [0, 1] and derive new upper bounds for Pickands' constant. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：142 / 147

页数：6

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