Stochastic Processes

Markov Chain Simulation

python
Run Inline
import numpy as np
# Define transition matrix
P = np.array([[0.7, 0.3],
              [0.4, 0.6]])
# Simulate chain
n_steps = 1000
states = np.zeros(n_steps, dtype=int)
for t in range(1, n_steps):
    states[t] = np.random.choice([0, 1], p=P[states[t-1]])
print(f"Proportion in state 0: {np.mean(states == 0):.3f}")

Stationary Distribution