Markov Chains: Convergence and Equilibrium

This lecture covers the convergence properties of Markov chains, focusing on the Law of Large Numbers and the equilibrium distribution. It explains the classical and Markov Laws of Large Numbers, the frequency of state visits, and the proof of the Markov Law of Large Numbers. The lecture also discusses the asymptotic behavior of Markov chains, the strong Markov property, and the computation of long-run mean rewards. Additionally, it explores the Perron-Frobenius theorem, periodicity, and the rate of convergence in Markov chains.