Fractional and Multifractional Brownian motion generator

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

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 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