Markov Chains: Theory and Applications

This lecture covers the theory and applications of Markov chains, focusing on topics such as discrete state space, transition matrices, probability mass functions, recurrent states, and periodic chains. The instructor explains the concepts of irreducibility, aperiodicity, positive recurrence, and invariant probability distributions. The lecture also delves into the properties of eigenvalues, eigenvectors, and the limiting behavior of Markov chains.