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Fractional Brownian motion generator

version (1.73 KB) by Zdravko Botev
Generates fractional Brownian motion with a given Hurst parameter using the FFT.


Updated 20 Jun 2016

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fast one dimensional fractional Brownian motion (FBM) generator
output is 'W_t' with t in [0,T] using 'n' equally spaced grid points;
code uses Fast Fourier Transform (FFT) for speed.
- Hurst parameter 'H' in [0,1]
- number of grid points 'n', where 'n' is a power of 2;
if the 'n' supplied is not a power of two,
then we set n=2^ceil(log2(n)); default is n=2^12;
- final time 'T'; default value is T=1;
- Fractional Brownian motion 'W_t' for 't';
- time 't' at which FBM is computed;
If no output it invoked, then function plots the FBM.
Example: plot FBM with hurst parameter 0.95 on the interval [0,10]
[W,t]=fbm1d(0.95,2^12,10); plot(t,W)
Kroese, D. P., & Botev, Z. I. (2015). Spatial Process Simulation.
In Stochastic Geometry, Spatial Statistics and Random Fields(pp. 369-404)
Springer International Publishing, DOI: 10.1007/978-3-319-10064-7_12

Comments and Ratings (1)

Sanghai Guan

Very good.


- bug fix (courtesy of Viktor Bezborodov): W=sqrt(T)*W ---> W=T^H*W; (unless final time T=1, this would affect the scaling).

- Vectorized for speed
- Written as an 'm' file with error control

MATLAB Release Compatibility
Created with R2015b
Compatible with any release
Platform Compatibility
Windows macOS Linux

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