Fractional and Multifractional Brownian motion generator

Version 1.2 (4.16 KB) by giannit
Generates Riemann-Liouville fractional and multifractional Brownian motion paths with a given Hurst function.
66 Downloads
Updated 11 May 2022

mBm

Generates Riemann-Liouville fractional and multifractional Brownian motion paths with a given Hurst function.

Matlab code available on github and View Multifractional Brownian motion generator on File Exchange

Here the animation generated by mBm_test.m

Usage

  • mbm = mBm(n,H,interval) produces a mBm path of length n with Hurst function H evaluated at the interval. If interval = [] then it is set to [0 1].
  • [mbm, ts] = mBm(n,H,interval) also produces the vector of the time steps.
  • [mbm, ts, hs] = mBm(n,H,interval) also produces the vector of the Hurst steps, i.e. the Hurst function evaluated at the interval.
  • [...] = mBm(n,H,interval,fig) plots the path and H if fig = true.

n = integer bigger than 1
H = function or real number between 0 and 1
interval = vector with two increasing components
fig = boolean

Examples

The first example plots a fBm path since H is constant (H=0.8), all the other examples plot mBm paths.

mBm(500, 0.8, [], true);
mBm(500, @(t) 0.6*t + 0.3, [], true);
mBm(500, @(t) 0.7 - 0.4 * exp(-64*(t-0.75).^2), [], true);
mBm(500, @(t) atan(t) / 3 + 0.5, [-pi pi], true);
mBm(500, @(t) sin(t) / 3 + 1/2, [0 4*pi], true);

Reference

S. V. Muniandy and S. C. Lim (2001)
Modeling of locally self-similar processes using multifractional Brownian motion of Riemann-Liouville type.
Physical Review E 63(4 Pt 2):046104
DOI: 10.1103/PhysRevE.63.046104

Cite As

giannit (2024). Fractional and Multifractional Brownian motion generator (https://github.com/Rabelaiss/mBm/releases/tag/1.2), GitHub. Retrieved .

MATLAB Release Compatibility
Created with R2021b
Compatible with any release
Platform Compatibility
Windows macOS Linux

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Version Published Release Notes
1.2

See release notes for this release on GitHub: https://github.com/Rabelaiss/mBm/releases/tag/1.2

1.1

See release notes for this release on GitHub: https://github.com/Rabelaiss/mBm/releases/tag/1.1

1.0

See release notes for this release on GitHub: https://github.com/Rabelaiss/mBm/releases/tag/1.0

To view or report issues in this GitHub add-on, visit the GitHub Repository.
To view or report issues in this GitHub add-on, visit the GitHub Repository.