Introduction to Stochastic Analysis WS 13/14
Prof. Dr. Anton Bovier
| Time and location: | Tuesdays, 8-10 We10/ Kleiner Hörsaal Fridays, 10-12 We10/ Kleiner Hörsaal |
|---|---|
| Beginning: | Tue. 14.10.2013 |
| Contact: | bovier@uni-bonn.de |
Content:
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
Prerequisits:
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.
Literature:
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.