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Fractional Brownian motion generator

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Fractional Brownian motion generator

by

Zdravko Botev (view profile)

 

06 Nov 2012 (Updated )

Generates fractional Brownian motion with a given Hurst parameter using the FFT.

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Description

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

Acknowledgements

This file inspired Fractional Brownian Field Or Surface Generator.

Required Products MATLAB
MATLAB release MATLAB 8.6 (R2015b)
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Updates
21 Jan 2016 2.0

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

20 Jun 2016 2.1

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

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