Ornstein-Uhlenbeck Process#

Simulate and visualise paths

# Author: Dialid Santiago <d.santiago@outlook.com>
# License: MIT
# Description: Simulate and visualise an Ornstein-Uhlenbeck Process

from aleatory.processes import OUProcess
from aleatory.styles import qp_style

qp_style()  # Use quant-pastel-style

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

$Ornstein–Uhlenbeck process $X(\theta=1.0, \sigma=0.5)$, Monte Carlo Simulated Paths $\{{X_t, t \in [t_0, T]\}}$, $X_T$ Marginal$

p = OUProcess(theta=1.0, sigma=1.0, initial=5.0, T=2.0)
fig = p.draw(n=200, N=200, figsize=(12, 7), colormap="Blues")
fig.show()

$Ornstein–Uhlenbeck process $X(\theta=1.0, \sigma=1.0)$, 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()

$Ornstein–Uhlenbeck process $X(\theta=1.0, \sigma=1.0)$$

Total running time of the script: (0 minutes 1.837 seconds)

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