New methods for simulation of fractional Brownian motion (Q1924856)

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.