T = 60

@jit

def time_path(T):

w = np.random.randn(T+1) # w_0, w_1, ..., w_T

def time_path(T, rng):

w = rng.standard_normal(T+1) # w_0, w_1, ..., w_T

w[0] = 0

b = np.zeros(T+1)

for t in range(1, T+1):

c = μ + (1 - β) * (σ * w - b)

return w, b, c

w, b, c = time_path(T)

rng = np.random.default_rng()

w, b, c = time_path(T, rng)

fig, ax = plt.subplots(figsize=(10, 6))

b_sum = np.zeros(T+1)

for i in range(250):

w, b, c = time_path(T) # Generate new time path

w, b, c = time_path(T, rng) # Generate new time path

rcolor = random.choice(('c', 'g', 'b', 'k'))

ax.plot(c, color=rcolor, lw=0.8, alpha=0.7)