File:OrnsteinUhlenbeckProcess2D.svg
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editDescriptionOrnsteinUhlenbeckProcess2D.svg |
English: 2D Ornstein-Uhlenbeck process with time step of .0001, while theta = 1.0 and sigma = 300. The initial position is (10, 10). Finally the point wanders around the central point (0, 0). |
Date | |
Source | Own work |
Author | Shiyu Ji |
Python/Matplotlib Code
edit# A simulation of 2D Ornstein-Uhlenbeck process with time step dt = .0001
import matplotlib.pyplot as pl
import numpy as np
t0 = 0.0
dt = 0.0001
t_final = 2
T = np.arange(t0, t_final, dt)
ax = pl.figure().add_subplot(111)
ax.set_xlabel('X')
ax.set_ylabel('Y')
x, y = 10.0, 10.0
ux, uy = 0.0, 0.0
theta = 1.0
sigma = 300.0
np.random.seed(1)
for t in T:
new_x = x + theta*(ux-x)*dt + sigma * np.random.normal(0, dt)
new_y = y + theta*(uy-y)*dt + sigma * np.random.normal(0, dt)
ax.plot([x, new_x], [y, new_y], 'b-', linewidth=0.5)
x, y = new_x, new_y
pl.show()
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This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 11:24, 11 November 2016 | ![]() | 720 × 540 (3.97 MB) | Shiyu Ji (talk | contribs) | User created page with UploadWizard |
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Width | 576pt |
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Height | 432pt |