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

Lecturer: Prof. Dr. Angelika Rohde

Assistant: Dr. Johannes Brutsche

Lecture: Mo and We 2-4 p.m., Albertstr. 23b

Exercise: Changed to Mo 4-6 p.m., SR 125/126, Ernst-Zermelo-Straße 1

Oral exam: Please contact Prof. Rohde to fix a date for this individually.

Language: english

Current

• As discussed in the lecture, we will switch tutorial sessions to Monday, 4pm in SR125/126, except for the 19th January and the last date, i.e. the remaining tutorials dates in 2026 are    

                      Mo 12.01.    Fr 16.01.    Mo 26.01.    Mo 02.02.     and     Fr 06.02.                                                                 

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. This exercise group is taking place on Friday 8-10 a.m. in SR 125/126 in the Institute of Mathematics, Ernst-Zermelo-Straße 1.

Lecture notes

Lecture notes (February, 4th) 

Exercise sheets

 
There will be weekly exercise sheets that have to be handed in. They will be issued on Wednesday, starting in the first week of the semester.

Please hand in your exercise sheet using the yellow mailbox 3.30 in the basement of the Institute of Mathematics.

You are allowed to hand in your solutions in groups of two.

For the pass/fail assessment (Studienleistung), you should earn at least 50% of the maximally accessible exercise points.

Literature

• Klaus-Jochen Engel und Rainer Nagel. A Short Course on Operator Semigroups , Springer.
• 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)