# A simulation of 1D Ito process with time step dt = .0001 # mu is zero. sigma is a Ricker wavelet. import matplotlib.pyplot as pl import numpy as np  t0 = 0.0 dt = 0.0001 t_final = 10.0 T = np.arange(t0, t_final, dt) ax = pl.figure().add_subplot(111) ax.set_xlabel('t') ax.set_ylabel('X')  x = 0.0 mu = 0.0 # Ito Integral np.random.seed(1)  def Ricker(t):     return 2.0/(np.sqrt(3)*(np.pi**.25))*(1-t*t)*np.exp(-0.5*t*t)  for t in T:     sigma = Ricker(t-t_final/2.0)     new_x = x + mu*dt + sigma * np.random.normal(0, dt)     ax.plot([t, t+dt], [x, new_x], 'b-', linewidth=0.5)     x = new_x  pl.show()