File:Wiener-process-trace.svg

Summary

Description
English: A sampled traces of a Wiener process with diffusion σ=1, D=1/2.
Date
Source Own work
Author Geek3
SVG development
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Source code
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Matplotlib source code

The plot was generated with Matplotlib
#! /usr/bin/env python3
# -*- coding:utf8 -*-

import matplotlib.pyplot as plt
import numpy as np
from math import *

plt.rcParams['font.sans-serif'] = 'DejaVu Sans'
np.random.seed(28)

a = 0. # starting value of X
sigma = 1. # diffusion
D = sigma**2 / 2 # diffusion constant
t = np.linspace(0, 3, 3001)

dt = t[1:] - t[:-1]
randnorm = np.random.normal(0, 1, len(t))
X = np.empty_like(t)
X[0] = a

for i in range(len(t) - 1):
    X[i+1] = X[i] + sigma * sqrt(dt[i]) * randnorm[i+1]

fig = plt.figure(figsize=(520 / 90.0, 340 / 90.0), dpi=72)
plt.plot(t, X)
plt.grid(True)
plt.xlim(t[0], t[-1])
plt.ylim(-3, 3)
plt.xlabel('t')
plt.ylabel('X')
plt.tight_layout()
plt.savefig('Wiener-process-trace.svg')

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Category:CC-BY-SA-4.0#Wiener-process-trace.svg
Category:Self-published work Category:Wiener process Category:Red noise
Category:CC-BY-SA-4.0 Category:Red noise Category:Self-published work Category:Valid SVG created with Matplotlib code Category:Wiener process