Fractional and Multifractional Brownian motion generator
mBm
Generates Riemann-Liouville fractional and multifractional Brownian motion paths with a given Hurst function.
Matlab code available on github and
Here the animation generated by mBm_test.m
Usage
-
mbm = mBm(n,H,interval)
produces a mBm path of lengthn
with Hurst functionH
evaluated at theinterval
. Ifinterval = []
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 theinterval
. -
[...] = mBm(n,H,interval,fig)
plots the path andH
iffig = 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
Cita come
giannit (2025). Fractional and Multifractional Brownian motion generator (https://github.com/Rabelaiss/mBm/releases/tag/1.2), GitHub. Recuperato .
Compatibilità della release di MATLAB
Compatibilità della piattaforma
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Versione | Pubblicato | Note della release | |
---|---|---|---|
1.2 | See release notes for this release on GitHub: https://github.com/Rabelaiss/mBm/releases/tag/1.2 |
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1.1 | See release notes for this release on GitHub: https://github.com/Rabelaiss/mBm/releases/tag/1.1 |
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1.0 | See release notes for this release on GitHub: https://github.com/Rabelaiss/mBm/releases/tag/1.0 |