Example of how to compute mean first passage times by brute force in parallel.

mfpt.py

from joblib import Parallel, delayed
import numpy as np

n = 10000                       # Number of experiments
dt: float = 1e-5                # Time step length


def integrate_until_exit(random_seed):
    np.random.seed(random_seed)

    t = 0.0
    x = np.zeros(2)

    while True:
        if np.linalg.norm(x) >= 1.0:
            break
        x += np.sqrt(dt) * np.random.randn(2)
        t += dt

    return t


fpts = Parallel(n_jobs=-1, verbose=1)(
    delayed(integrate_until_exit)(i) for i in range(n))

print('MFPT', np.mean(fpts), '+/-', np.std(fpts))