The Weierstrass–Mandelbrot Process Revisited

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• 作者：Szulga ; Jerzy ; Molz ; Fred
• 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
• 刊名：Journal of Statistical Physics
• 出版年：2001
• 出版时间：2001
• 年：2001
• 卷：104
• 期：5/6
• 页码：1317-1348
• 全文大小：260 KB

文摘

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.