Advanced Probability Theory

Based on the rigorous foundations of probability theory, hinging on measure and integration theory, this course covers a number of topics and methods from the theory of probability that are all of crucial importance for modern probability theory. The most significant subjects covered in the course include: Convergence in probability and in distribution, Fourier transforms and characteristic functions, The Central Limit Theorem, series of independent random variables, The Strong Law of Large Numbers, conditional expectations, martingales, submartingales and supermartingales.