File:OrnsteinUhlenbeckProcess2D.svg

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Description
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

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# 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()

Licensing

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I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

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Date/TimeThumbnailDimensionsUserComment
current11:24, 11 November 2016Thumbnail for version as of 11:24, 11 November 2016720 × 540 (3.97 MB)Shiyu Ji (talk | contribs)User created page with UploadWizard

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