LFU:online

Students who have completed the course have an overview over some of the recent questions in advanced probability theory and the methods used to solve these problems. They have acquired a deeper understanding of probability theory and are able to analyse and solve typical problems in the field.

Martingales: definition and examples, optional sampling, martingale convergence and  L^p-martingales;

Brownian motion: definition and existence, Markov property and martingale property, strong Markov property, reflection principle, strong law of large numbers for Brownian motion, weak convergence in C([0,1]), Donsker's theorem;

Poisson processes: definition and existence, spaces of point measures, weak convergence of point processes

Lecture, assessment is based on a single examination at the end of the course.

Course examination according to § 7, statute section on "study-law regulations"

Billingsley - Convergence of Probability Measures

Durrett - Probability and Examples

Mörters, Peres - Brownian Motion

Resnick - Extreme Values, Regular Variation, and Point Processes

Stochastik 1 and Stochastik 2

-