# 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()