Advanced Probability Theory - Einzelansicht

 The students are weekly invited to

1-  read and prepare first alone at home some precise topics (indicated on the Moodle page)

2- participate to the two lessons during which Prof. Sylvie Roelly present the topics, prove the theorems and comments them

3- solve an Exercise sheet, and participate to a meeting with Dr. Peter Keller where the solutions are discussed.

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Precise data (literature, timetable etc) are given on the corresponding Moodle web-page

https://moodle2.uni-potsdam.de/course/view.php?id=25305 

The main reference is

Durrett, R. : Probability: theory and examples.

Cambridge Series in Statistical and Probabilistic Mathematics 2010

Every one is advised to read the general informations written on the moodle plattform "Introductory to Master in Mathematics".

The participant is assumed to have a reasonable grasp of 
probability theory, analysis, functional analysis and measure theory.

Written or oral exam

The purpose of this course is to treat in detail selected fundamentals of modern probability theory. The focus is in particular on limit theorems including the strong law of large numbers, Lindeberg's central limit theorem and Poisson convergence. We will also introduce and study discrete-time martingales. Various examples will be considered.

The participant is assumed to have a reasonable grasp of basic probability, analysis 1-4, and measure theory.

This lecture is appropriate for Master students or for advanced Bachelor students. It is a natural extension of the course "Stochastik" and an application of the course "Functional Analysis I".

It is part of both profiles "Mathematical modeling and data analysis" and "Structures of Mathematics with physical background" in the course of studies Master of Science Mathematics.

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.