Probability with Martingales WS 2023/24
Wintersemester / winter term 2023/24
| Modul | Mathematik Master-Modul: MA-20 Probability with Martingales |
| Dozent / Lecturer | Prof. Dr. René Schilling |
| Umfang / contact | 3+1 |
| OPAL | OPAL-Course (please register) |
| Ort / venue | see Zeit/time |
| Zeit / time | Mon 2DS = 09:20 - 10:50, WIL/A124 Tue 5DS = 14:50 - 16:20, REC/C118 |
| Übungen / tutorials | included in the lectures |
| Beginn / begin | first week of term |
| Niveau / level | Master / MSc |
| Unterrichtssprache / language |
English |
| Prüfung / exam | oral examination (approx. 20 min/person) Ort & Zeit / Venue & Time: last week of term or first week after term Anmeldung / registration: via the exam office Hilfsmittel / resources: n/a |
| Prüfungsamt / exam office |
Homepage Aktuelles |
- This course is the foundation course for all further studies in probability theory and stochastics. We will further develop the theory of discrete martingales (started in the course on probability theory for BSc), discuss the CLT and then move on to Brownian motion. As a follow-up, I will read a course on stochastic calculus (Brownian Motion, Ito Integral, Stochastic differential equations) and a seminar (WIA) on Lévy processes.
- You will regularly get problems for solution, problems and full solutions will appear on OPAL. A random selection of these problems will serve as a basis for the oral exam at the end of the course.
- Prerequisites: Measure & Integration (as in Ba-AN30) and BSc-level probability (as in ST-10). Alternatively, Chapters I-VII and IX.38-40 in my lecture notes Measure, Integral, Probability & Processes (see below).
- Recommended Reading
- (lecture notes) Schilling: Measure, Integral, Probability, & Processes. Amazon Kindle Self-Publishing, Dresden 2021.
ISBN: 979-8-5991-0488-9 [www.tinyurl.com/rlscourse] - (textbook) Schilling: Brownian Motion. A Guide to Random Processes and Stochastic Calculus. 3rd edn. De Gruyter, Berlin 2021. ISBN: 978-3-11-074124-4.
[Zur hompage des Buchs] - (textbook) Williams: Probability with Martingales. Cambridge University Press, Cambridge 1991. ISBN: 978-0-521-40605-5.
- (lecture notes) Schilling: Measure, Integral, Probability, & Processes. Amazon Kindle Self-Publishing, Dresden 2021.
- Online material via OPAL
© Robert Lohse
Prof. Dr. René Schilling
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Visiting address:
Bürogebäude Z21, room 326.2 Zellescher Weg 25
01217 Dresden