250113 VO Advanced probability theory (2017S)

Many basic notions and results of probability can only be rigorously
formalised and analysed once measure theory is available. The lectures
offer an introduction to this "advanced" theory. We shall discuss the
existence of suitable models, and the most important limit theorems for
sequences of random variables, like the law of large numbers (and, more
generally, the ergodic theorem), the central limit theorem and extensions
(e.g. to function spaces), and study some important types of stochastic
processes (including Brownian motion).