Stationary Distribution in Markov Chains

This lecture covers examples of stationary distribution in Markov chains, focusing on the cyclic random walk. It explains the concept of positive-recurrent chains, the existence and uniqueness of the stationary distribution, and provides proofs and counter-examples. The lecture also discusses the case of irreducible and reducible chains, highlighting the implications on the existence and uniqueness of the stationary distribution. Additionally, it explores the scenario where the chain is not irreducible, leading to the presence of multiple transient classes. The importance of understanding the stationary distribution in Markov chains is emphasized throughout the lecture.