For MA-M, MA-LG, DM, DP
(Modulnummer A710, A750, 82j, 83j, MAT-VM-D731, MAT-VM-D831-35, MAT-VM-D931-33)
The course of Stochastic Analysis builds close links between probability theory and calculus.
At the beginning of the course, the fundamental process of Brownian motion will be constructed. The Markov and martingale properties of this process will be studied and discussed in detail. A stochastic integral and differential calculus will be introduced. These will be used to solve (linear) stochastic differential equations (explicitly). A number of important examples and applications in the natural sciences will be considered.
Complementing the lecture course is a 2-hour seminar on stochastic analysis.
The lecture is part of the profile direction "Mathematische Modellierung und Datenanalyse" in the Master of Science programme in mathematics.
- Deck, T. Der Itô-Kalkül, Springer 2006
- Durett, R. Essentials of stochastic processes, 1999
- Klenke, A. Probability Theory, A Comprehensive Course, 2. Auflage Springer 2014
Prof. Dr. Roelly