random_walk_simulation.py

import numpy as np
np.random.seed(1234)

def random_walk(N):
    """
    Simulates a discrete random walk
    :param int N : the number of steps to take
    """
    # event space: set of possible increments
    increments = np.array([1, -1])
    # the probability to generate 1
    p=0.5
    
    # the epsilon values
    random_increments = np.random.choice(increments, N, p)
    # calculate the random walk
    random_walk = np.cumsum(random_increments)
    
    # return the entire walk and the increments
    return random_walk, random_increments
  
  # generate a random walk
N = 500
X, epsilon = random_walk(N)

# normalize the random walk using the Central Limit Theorem
X = X * np.sqrt(1./N)