Explores the concept of martingales and their relation to Brownian motion through symmetric simple random walks and discusses the potential positive outcomes from the current crisis.
Covers Markov processes, transition densities, and distribution conditional on information, discussing classification of states and stationary distributions.
Explores convergence criteria for martingales, including almost sure convergence and Cauchy criterion, leading to the first martingale convergence theorem.
Introduces Hidden Markov Models, explaining the basic problems and algorithms like Forward-Backward, Viterbi, and Baum-Welch, with a focus on Expectation-Maximization.
