Markov Chains: States Classification

This lecture covers the classification of states in Markov chains, introducing the concept of communicating classes and absorbing states. It explains hitting times, hitting probabilities, and the calculation of expected hitting times. The lecture also delves into birth and death chains, illustrating first transition analysis and absorption probabilities. The instructor demonstrates the application of these concepts through examples like Gambler's Ruin, emphasizing the importance of understanding the probability of reaching certain states. The lecture concludes with discussions on homogeneous difference equations and the expected duration of games in various scenarios.