The purpose of this course is to treat in details selected fundamentals of modern probability theory. The focus is in particular on limit theorems including the strong law of large numbers and Lindeberg's 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 basic probability, basic analysis and measure theory.
This lecture is appropriate for Master students or for advanced Bachelor students. It is a natural application/extension of the course "Functional Analysis I".
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.
The lecture also adresses to students of informatics and physics.Literature:
|Durrett, R. Probability: theory and examples, Cambridge Series in Statistical and Probabilistic Mathematics 2010|
"Stochastik" or "Foundations of stochastics", optimal "Functional Analysis 1"
Prof. Dr. Sylvie Roelly
(First lecture: Wed 10.04.19)
Dr. Tania Kosenkova
Fri., 14:15-15:45, 2.09.014