Chiara Franceschini
Summary: I gave a course on discrete time Markov chains. In particular, I have discussed the Markov property and its strong version for stopping time. We spent some time discussing the different states a Markov chain can be, giving different conditions for recurrence (positive and null) and transience. We have manly focus on Markov chains with finite state space: for these we have seen conditions for the existence, the uniqueness and convergence to the stationary distributions. Without proving we have extended the result for infinite state space as well. We ended with the notion of reversibility. Throughout the course we have seen some typical examples of Markov chains: in particular the so-called gambler’s ruin the symmetric and asymmetric random walk on Z.