Lecture
This lecture covers the concept of stationary distribution in Markov chains, defining it as the distribution at time n, and explaining its existence and properties. The instructor discusses the implications of a stationary distribution, such as the equality T.P = T.P and the conditions for positive-recurrence. Mathematical remarks are made regarding column vectors and stochastic matrices, leading to theorems and corollaries about the positive-recurrence of Markov chains and the existence of unique stationary distributions. The lecture concludes with practical remarks on the uniqueness and existence of stationary distributions in Markov chains.