File:WienerProcess3D.svg
Summary
| Description |
English: A single sample path of a three-dimensional Brownian motion (Wiener process) Wt, as generated by Wolfram Mathematica with a time step of size 0.0001, for times 0 ≤ t ≤ 2. |
| Date | |
| Source | Own work based on: Wiener process 3d.png |
| Author | Shiyu Ji |
| SVG development |
Python/Matplotlib Code
# A simulation of Wiener process with time step dt = .0001
from mpl_toolkits.mplot3d import axes3d
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, projection='3d')
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
x, y, z = 0.0, 0.0, 0.0
np.random.seed(1)
for t in T:
new_x = x + np.random.normal(0, dt)
new_y = y + np.random.normal(0, dt)
new_z = z + np.random.normal(0, dt)
ax.plot([x, new_x], [y, new_y], [z, new_z], 'b-', linewidth=0.5)
x, y, z = new_x, new_y, new_z
pl.show()
Licensing
Shiyu Ji, the copyright holder of this work, hereby publishes it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
Attribution:
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- 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.
