Probability with Martingales WS 2026/27

Wintersemester / winter term 2026/27

• This course is the foundation course for all further studies in probability theory and stochastics. We will further develop the theory of discrete and continuous-time martingales (started in the course on probability theory for BSc) and then move on to Brownian motion.
• 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.39-41 in my lecture notes Measure, Integral, Probability & Processes (see below).
• Recommended Reading
  • (lecture notes) Schilling: Measure, Integral, Probability, & Processes (2nd ed = blue cover). Amazon Kindle Self-Publishing, Dresden 2025.
    ISBN: 979-8-2697-8920-0 [Homepage of this Book]
  • (textbook) Schilling: Brownian Motion. A Guide to Random Processes and Stochastic Calculus. 3rd edn. De Gruyter, Berlin 2021. ISBN: 978-3-11-074124-4.
    [Homepage of this Book]
  • (textbook) Revuz & Yor: Continuous Martingales and Brownian Motion (3rd edn). Springer, Berlin 1999. ISBN 3-540-64325-7.
  • (textbook) Rogers & Williams: Diffusions, Markov Processes, and Martingales. Cambridge University Press, Cambridge 2000. ISBN  978-1-107-71520-2.
  • (textbook) Williams: Probability with Martingales. Cambridge University Press, Cambridge 1991.  ISBN: 978-0-521-40605-5.
• Online material via OPAL

© Robert Lohse

Name

Prof. Dr. René Schilling

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Institute of Mathematical Stochastics

Institute of Mathematical Stochastics

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Bürogebäude Z21, room 326.2 Zellescher Weg 25

01217 Dresden

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