Prof. Dr. Anton Bovier
|Time and location:||Tuesdays, 8-10 We10/ Kleiner Hörsaal|
Fridays, 10-12 We10/ Kleiner Hörsaal
This course gives an introduction to the theory of stochastic analysis.
The following key concepts are covered:
- Brownian motion
- Continuous time martingales
- Weak convergence and tightness
- Stochastic integrals
- Stochastic differential equations
- Dirichlet problems
The course builds on the lectures "Einführung in die Wahrscheinlichkeitstheorie" and "Stochastic processes". Lecture notes for both courses are available on my homepage. You are expected to have a reasonable knowledge of measure theory, know what conditional expectations are, have seen the construction of stochastic processes through the Daniell-Kolmogorov theorem, know key properties of martingales in discrete time, stopping times, and Markov processes. The cours is suitable for Bachelor students and as a foundations module for beginning Master students.
A preliminary version of the lecture notes is available. There will be updates as we go along. For further reading, see the references given there.