Stochastic Differential Equations (4V+2U, 9.0 LP)
|SWS||Type||Course Form||CP (Effort)||Presence-Time / Self-Study|
|-||K||Lecture with exercise classes (V/U)||9.0 CP||186 h|
|2||U||Exercise class (in small groups)||28 h|
|(4V+2U)||9.0 CP||84 h||186 h|
|CP, Effort||9.0 CP = 270 h|
|Position of the semester||1 Sem. irreg. WiSe|
|Level|| Master (Advanced)|
+ further Lecturers of the department Mathematics
|Area of study||[MAT-SPAS] Analysis and Stochastics|
The course is offered at least every second winter semester.
Stochastic differential equations (SDEs) are used for modelling continuous-time random phenomena.
Key elements of the theory of stochastic differential equations are discussed. In addition, an introduction to algorithmic aspects is given. The following topics are covered:
- Brownian motion,
- martingales theory,
- stochastic integration (with respect to Brownian motion),
- strong and weak solutions of SDEs,
- stochastic representation of the solution of partial differential equations,
- classical approximations,
- stochastic multi-level algorithms.
- I. Karatzas, S. E. Shreve: Brownian Motion and Stochastic Calculus,
- P. E. Kloeden, E. Platen: Numerical Solution of Stochastic Differential Equations,
- T. Müller-Gronbach, E. Novak, K. Ritter: Monte-Carlo-Algorithmen.
Further literature will be announced in the lecture; Exercise material is provided.
Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).
Requirements for attendance (informal)
Basic knowledge in Functional Analysis, e.g. from the course [MAT-12-23-K-3].
- [MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)
- [MAT-60-11-M-4] Probability Theory (M, 9.0 LP)
Requirements for attendance (formal)