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.
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页码：369 / 384
页数：16
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