A WAVELET-BASED ALMOST-SURE UNIFORM APPROXIMATION OF FRACTIONAL BROWNIAN MOTION WITH A PARALLEL ALGORITHM

被引：0

作者：

Hong, Dawei ^{[1
]}

Man, Shushuang ^{[2
]}

Birget, Jean-Camille ^{[1
]}

Lun, Desmond S. ^{[1
]}

机构：

[1] Rutgers State Univ, Dept Comp Sci, Ctr Computat & Integrat Biol, Camden, NJ 08102 USA

[2] Southwest Minnesota State Univ, Dept Math & Comp Sci, Marshall, MN 56258 USA

来源：

JOURNAL OF APPLIED PROBABILITY | 2014年 / 51卷 / 01期

关键词：

Fractional Brownian motion; wavelet expansion of stochastic integral; almost-sure uniform approximation; GAUSSIAN-PROCESSES; SERIES EXPANSION; WEAK-CONVERGENCE; OPTIMALITY; SHEET;

D O I：

暂无

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 construct a wavelet-based almost-sure uniform approximation of fractional Brownian motion (FBM) (B-t((H)))(t is an element of[0,1]) of Hurst index H is an element of (0, 1). Our results show that, by Haar wavelets which merely have one vanishing moment, an almost-sure uniform expansion of FBM for H is an element of (0, 1) can be established. The convergence rate of our approximation is derived. We also describe a parallel algorithm that generates sample paths of an FBM efficiently.

引用

页码：1 / 18

页数：18

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