Jump to content

File:ItoWienerProcess2D.svg

Page contents not supported in other languages.
This is a file from the Wikimedia Commons
From Wikipedia, the free encyclopedia

Original file (SVG file, nominally 720 × 540 pixels, file size: 7.92 MB)

Summary

Description
English: A simulation of 2D Ito and Wiener processes.
Date
Source Own work
Author Shiyu Ji

Python/Matplotlib Code

# A simulation of 2D drifted Wiener 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 = 0.0, 0.0
mu = .02
sigma = 1.0
# drifted Wiener's (also Ito's)
np.random.seed(1)
for t in T:
    new_x = x + mu*dt + sigma * np.random.normal(0, dt)
    new_y = y + mu*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

# Wiener's
x, y = 0.0, 0.0
np.random.seed(1)
for t in T:
    new_x = x + sigma * np.random.normal(0, dt)
    new_y = y + sigma * np.random.normal(0, dt)
    ax.plot([x, new_x], [y, new_y], 'r-', linewidth=0.5)
    x, y = new_x, new_y

pl.show()

Licensing

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.

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts

11 November 2016

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current12:58, 11 November 2016Thumbnail for version as of 12:58, 11 November 2016720 × 540 (7.92 MB)Shiyu JiUser created page with UploadWizard

The following page uses this file:

Global file usage

The following other wikis use this file:

Metadata