A strong uniform approximation of fractional Brownian motion by means of transport processes

被引：12
|
作者：
Garzon, J. [1 ]
Gorostiza, L. G. [1 ]
Leon, J. A. [2 ]
机构：
[1] CINVESTAV, Dept Math, Mexico City 07000, DF, Mexico
[2] CINVESTAV, Dept Automat Control, Mexico City 07000, DF, Mexico
来源：
STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2009年 / 119卷 / 10期
关键词：
Fractional Brownian motion; Transport processes; Almost sure convergence; Rate of convergence; CONVERGENCE;
D O I：
10.1016/j.spa.2009.06.003
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 Sequence of processes that converges strongly to fractional Brownian motion uniformly on bounded intervals for any Hurst parameter H, and we derive a rate of convergence, which becomes better when H approaches 1/2. The construction is based on the Mandelbrot-van Ness stochastic integral representation of fractional Brownian motion and on a strong transport process approximation of Brownian motion. The objective of this method is to facilitate Simulation. (C) 2009 Elsevier B.V. All rights reserved.
引用
收藏
页码：3435 / 3452
页数：18
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