Probability Theory

SS 2023



Tuesday, 16:00 - 18:00, M2
Thursday, 16:00 - 18:00, M2
First lecture: Tuesday, 04.04.2023
Lecturer:  Prof. Chiranjib Mukherjee
Assistance:  Luzie Kupffer
Course overview: This course in the course overview
The tutorials in the course overview
Course syllabus:

We will start by embedding probability theory into a general framework, where we will construct infinite sequences of independent random variables, and (re)visit laws of large numbers, 0-1 laws and  the central limit theorem for independent and identically distributed random variables.

In order to be able to study more general sequences of random variables we will introduce the concept of conditional expectation, prove Randon-Nikodym theorem and Lebesgue decompisition theorem. With this background, we will then provide the theory of martingales and that of Markov chains.

Prerequesites: Some familiarity with measure theory and  Stochastics will be helpful (Notes from the Stochastics lecture in WS 2022-23, where this background was covered, will be available in Learnweb). Please do contact us if you have any questions and/or concerns regarding your background.
Learnweb: Please enroll in the Learnweb course for this lecture.
Course assessment: TBA