The purpose of this course is to treat in detail select fundamentals of modern probability theory.
Particular focus is given to limit theorems -- including the strong law of large numbers and Lindeberg central limit theorem -- and on discrete-time processes like martingales, as well as basic results on Brownian motion. Various examples will be considered.
The participant is assumed to have a reasonable grasp of probability, analysis, functional analysis and measure theory. This lecture is appropriate for Master students in Mathematics and for advanced Bachelor students in Mathematics. It also adresses to students of Data Science, Informatics and Physics.
It is part of both profiles "Mathematical modelling and data analysis" and "Structures of Mathematics with physical background" in the course of studies Master of Science Mathematics.
Lectures: Prof. Dr. Sylvie Roelly
Exercises: Alexander Zass