Bounds for expected maxima of Gaussian processes and their discrete approximations

被引：24

作者：

Borovkov, Konstantin ^{[1
]}

Mishura, Yuliya ^{[2
]}

Novikov, Alexander ^{[3
,4
]}

Zhitlukhin, Mikhail ^{[4
]}

机构：

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

[2] Taras Shevchenko Natl Univ Kyiv, Mech & Math Fac, Kiev, Ukraine

[3] Univ Technol Sydney, Sch Math & Phys Sci, Sydney, Australia

[4] Steklov Inst Math, Moscow, Russia

来源：

STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES | 2017年 / 89卷 / 01期

基金：

澳大利亚研究理事会; 俄罗斯科学基金会;

关键词：

Expected maximum; Gaussian processes; fractional Brownian motion; discrete approximation; processes with long memory; 60G15; 60G22; 60J65; BROWNIAN-MOTION;

D O I：

10.1080/17442508.2015.1126282

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper deals with the expected maxima of continuous Gaussian processes that are Holder continuous in norm and/or satisfy the opposite inequality for the norms of their increments. Examples of such processes include the fractional Brownian motion and some of its relatives (of which several examples are given in the paper). We establish upper and lower bounds for and investigate the rate of convergence to that quantity of its discrete approximation. Some further properties of these two maxima are established in the special case of the fractional Brownian motion.

引用

页码：21 / 37

页数：17

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