Stochastic Processes
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# Stochastic Processes ## Markov Chain Simulation ## Stationary Distribution Solve $\pi P = \pi$ with $\sum \pi_i = 1$. [Join Discord](https://discord.gg/gE2m4Qrdqv) [Previous**MCMC**](/notes/04-degree-electives-bsma3014-statistical-computing-week06-06-mcmc)[Next**Numerical Linear Algebra**](/notes/04-degree-electiv...
Stochastic Processes
Markov Chain Simulation
pythonimport 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}")