New methods for simulation of fractional Brownian motion
type: Item
instance of: scholarly article
title: New methods for simulation of fractional Brownian motion
zbMATH Open document ID: 0859.65145
author: Yanyan Li
published in: Journal of Computational Physics
publication date: 1997-04-15T00:00:00Z
review text: Fractional Brownian motion (fBm) occurs in the modeling of physical processes with a certain persistence. The increments \(W_H(x)= B_H(x+\Delta x)-B_H(x)\) of one-dimensional fBm \(B_H\) with index \(H\) \((0<H<1)\) form a stationary process with variance \(r_0\Delta x^{2H}\). The process \(W_H\) is called fractional white noise. It is simulated efficiently on the basis of a classical spectral method using the fast Fourier transforms. Then \(B_H\) is obtained by summation. The turning bands method is introduced to simulate two- and three-dimensional fBm. The line process in the turning bands method must be a one-dimensional fBm but with the variance multiplied by a certain factor which depends on \(H\) and on the dimension of the process. These algorithms are accurate and efficient.
Mathematics Subject Classification ID: 65C99
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 938008
zbMATH Keywords: fractional Brownian motion
zbMATH Keywords: stationary process
zbMATH Keywords: spectral method
zbMATH Keywords: fast Fourier transforms
zbMATH Keywords: turning bands method
zbMATH Keywords: algorithms
reviewed by: Rudolf Wegmann
MaRDI profile type: Publication
OpenAlex ID: W2049963749
DOI: 10.1006/JCPH.1996.0158
description: scientific article; zbMATH DE number 938008