Information on the lecture Probability Theory II (WS 2025/2026)

Lecture: Mo., We., 14-16 a.m., Albertstr. 23b

Exercise: 2 hours, date to be determined

Written exam:

Language: english

Current

Content

A stochastic process is a family of random variables, where mostly the situation T = ℕ or T = [0, 1] is studied. Basic examples include stationary time series, the Poisson process and Brownian motion as well as processes derived from those. The lecture includes ergodic theory and its applications, Brownian motion and especially the study of its path properties, Markov processes, the elegant concept of weak convergence on Polish spaces as well as functional limit theorems. Finally, we introduce stochastic integration with respect to local martingales, based on the continuous time version of the martingale transform.

Exercise groups

There will be an exercise group to discuss the solutions of the weekly exercises.

Lecture notes

Exercise sheets

Literature

Olav Kallenberg. Foundations of Modern probability, Springer.
Achim Klenke. Wahrscheinlichkeitstheorie, Springer.

Usability

Wahlmodul im Optionsbereich (2HfB21)
Wahlpflichtmodul Mathematik (BSc21)
Angewandte Mathematik (MSc14)
Mathematik (MSc14)
Vertiefungsmodul (MSc14)
Wahlmodul (MSc14)
Advanced Lecture in Stochastics (MScData24)
Elective in Data (MScData24)

Consultation hour

Lecturer consultation hours: Tuesday, 4 p.m. (or by arrangement)
Consultation hour assistant: Tuesday, 2 p.m. (or by arrangement)