Fractional Brownian motion

A header only C++ library for generating fractional Brownian motion in 1D, 2D and 3D (the latter two are technically variants of a fractional Brownian bridge).

We focus on fast implementation, therefore, we can only generate for lengths that are a power of 2.

This library is mainly used from within the Alsvinn simulator.

Also comes with a Python library (requiresboost::python and boost::numpy).

Requirements

• A C++11 compatible compiler (tested with GCC and Clang)
• cmake >= 3.10.0 (optional)
• boost >= 1.67.0 (optional) only for python and tests
• python (optional) for python bindings
• doxygen (optional) for documentation

Running from Python

Make sure the folder fbmpy from the build folder is in your PYTHONPATH. Then from Python you can do something like:

import fbmpy
import numpy as np
import matplotlib.pyplot as plt

# Plain old Brownian motion
Hurst_index = 0.5

N = 128
X = np.random.normal(0, 1, N)
d = fbmpy.fractional_brownian_motion_1d(Hurst_index, N, X)
x = np.linspace(0, 1, N+1)
plt.plot(x, d)
plt.show()