1) Prerequisites
No formal requirements. We assume prior knowledge of elementary measure theory in a probabilistic context. It is recommended to take the course Measure Theoretic Probability before.
2) Aim of the course
This course provides a rigorous, measure-theoretic introduction to the theory of stochastic processes. Building on a solid foundation in probability theory, the course develops the mathematical framework necessary to understand randomness as it evolves over time. Topics include fundamental properties (e.g., Mecke equation) of Poisson processes, construction of Brownian motion, discrete- and continuous-time martingales, and foundations of Markov and Feller processes. The course is intended to prepare students for advanced study and research in probability, stochastic geometry, financial mathematics, and related fields.
3) Rules about Homework/Exam
This course includes optional homework assignments and a final oral examination. The homework is intended as practice and will not contribute to the final grade. The final grade will be based entirely on the final oral exam (or, if applicable, the retake).
4) Lecture notes/Literature
The course is partly based on lecture notes of Harry van Zanten. Moreover, we recommend the books Continuous Martingales and Brownian Motion by Daniel Revuz and Marc Yor as well as Lectures on the Poisson Process by G\"unter Last and Mathew Penrose.
5) Lecturer
Moritz Otto
- Docent: Sonja Cox
- Docent: Asma Khedher