Fractional Brownian Motion#

Simulate and visualise paths

# Author: Dialid Santiago <d.santiago@outlook.com>
# License: MIT
# Description: Simulate and visualise a Fractional Brownian Motion

from aleatory.processes import fBM
from aleatory.styles import qp_style

qp_style()  # Use quant-pastel-style

p = fBM()
fig = p.draw(n=200, N=200, figsize=(12, 7), colormap="viridis")
fig.show()

$Fractional Brownian Motion $X = B_{0.5}(t)$, Monte Carlo Simulated Paths $\{{X_t, t \in [t_0, T]\}}$, $X_T$ Marginal$

p = fBM(hurst=0.25, T=2.0)
fig = p.draw(n=200, N=200, figsize=(12, 7), colormap="seismic")
fig.show()

$Fractional Brownian Motion $X = B_{0.25}(t)$, Monte Carlo Simulated Paths $\{{X_t, t \in [t_0, T]\}}$, $X_T$ Marginal$

fig = p.plot(n=100, N=10, figsize=(12, 7))
fig.show()

$Fractional Brownian Motion $X = B_{0.25}(t)$$

Total running time of the script: (0 minutes 2.059 seconds)

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