Voortgezette Kansrekening

The goal of the course is to extend the basic notions of probability with an analytic toolkit.

Rigorous probability is closely related to real and complex analysis. We will explore these connections and learn how concepts from real analysis translate to probability and vice versa.

In particular we will construct a general probability space and perform computations of expectations, and conditional expectation of random variables therein.

We will treat different types of convergences of random variables, Borel-Cantelli Lemmas, Kolmogorov's 0-1 law.

We will learn various analytic methods to prove convergence or random variables: characteristic functions, Fourier inversion, generating function. Laws of Large Numbers and general Central Limit Theorems will be discussed. If time permits, we will learn about stable distributions.