drifted_bm.py

import numpy as np

def drifted_brownian_motion(mu, sigma, N, T, seed=42):
    """Simulates a Brownian Motion with drift.
    
    :param float mu: drift coefficient
    :param float sigma: volatility coefficient
    :param int N : number of discrete steps
    :param int T: number of continuous time steps
    :param int seed: initial seed of the random generator
    :returns list: drifted Brownian motion
    """
    # set the seed
    np.random.seed(seed)
    # standard brownian motion
    W, _ = brownian_motion(N, T ,1.0)
    # the normalizing constant
    dt = 1. * T/N
    # generate the time steps
    time_steps = np.linspace(0.0, N*dt, N+1)
    # calculate the Brownian Motion with drift
    X = mu * time_steps + sigma * W
    return X