Convergence of the Weierstrass-Mandelbrot process to fractional Brownian motion

被引：15

作者：

Pipiras, V ^{[1
]}

Taqqu, MS ^{[1
]}

机构：

[1] Boston Univ, Dept Math, Boston, MA 02215 USA

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2000年 / 8卷 / 04期

关键词：

Weierstrass function; Weierstrass-Mandelbrot process; fractional Brownian motion; functional central limit theorem; strong mixing; martingale difference sequences;

D O I：

10.1142/S0218348X00000408

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this work, we develop Mandelbrot's idea that Weierstrass's nowhere differentiable function can be modified and randomized to approximate fractional Brownian motion (FBM). Our approach covers the convergence of processes of a more general type and allows us to consider different dependence structures in the above randomization.

引用

页码：369 / 384

页数：16

共 14 条

[1]

[Anonymous], MATEMATISCHE WERKE

[2] ON THE WEIERSTRASS-MANDELBROT FRACTAL FUNCTION [J].