Theoretical Aspects of Stochastic Processes

Course content

Introduction to stochastic processes. Emergence and applications of stochastic processes in various areas of mathematics such as geometry and group theory. Finite and countable Markov chains. Classification of states with proofs. Continuous-time Markov chains; Poisson process. Conditional expectation. Martingales. Brownian motion. Fractal nature of zero sets of Brownian motion.