Advanced Stochastic Processes

Course outline:
This course is a third year module for students studying Actuarial Science or Mathematical Statistics, though not a requirement for a major in Mathematical Statistics. The course gives a theoretical overview of stochastic processes with the models covered spanning both discrete and continuous time as well as discrete and continuous state-space. Though the emphasis is on the theoretical properties of the models, the application of the methods to real-world problems is also explored at length. Topics covered include: Poisson processes, continuous-time Markov chains, random walks, probability theory, discrete-time martingale processes, Brownian motion and diffusion processes.