1611.sagews

print 'approaching brownian motion through limit of scaled random walk'

import numpy as np
mu, sigma = 0, 1 # mean and standard deviation
nmax = 1000;
s = np.random.normal(mu, sigma, nmax)
#s = np.random.standard_cauchy(nmax)
ss = np.cumsum(s)
import matplotlib.pyplot as plt

@interact
def f( n=(1..nmax) ):
    P = points([(i/n, 1/sqrt(n)*ss[i+1] ) for i in range(0, n)])
    P.set_axes_range(0, 1, -2, 2)
    show(P)

approaching brownian motion through limit of scaled random walk