## Fractional Brownian motion generator

Version 2.1.0.0 (1.73 KB) by
Generates fractional Brownian motion with a given Hurst parameter using the FFT.

Updated 20 Jun 2016

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.
INPUT:
- 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;
OUTPUT:
- 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)
Reference:
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

### Cite As

Zdravko Botev (2023). Fractional Brownian motion generator (https://www.mathworks.com/matlabcentral/fileexchange/38935-fractional-brownian-motion-generator), MATLAB Central File Exchange. Retrieved .

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

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
Version Published Release Notes
2.1.0.0

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

2.0.0.0

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

1.0.0.0