The Weierstrass-Mandelbrot process revisited

被引：16

作者：

Szulga, J ^{[1
]}

Molz, F

机构：

[1] Auburn Univ, Dept Math, Auburn, AL 36849 USA

[2] Clemson Univ, Dept Environm Sci, Clemson, SC USA

来源：

JOURNAL OF STATISTICAL PHYSICS | 2001年 / 104卷 / 5-6期

基金：

美国国家科学基金会;

关键词：

fractional Brownian motion; Brownian motion; Weierstrass-Mandelbrot process; stationary increments; structure functions; Gaussian processes; self-similar processes; quasi-Gaussian processes; spectral representation; power spectrum;

D O I：

10.1023/A:1010422315759

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We derive a functional central limit theorem for quasi-Gaussian processes. In particular, we prove that the limit of the Mandelbrot-Weierstrass process is a complex fractional Brownian motion.

引用

页码：1317 / 1348

页数：32

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