Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-64-11-K-7

Stochastic Differential Equations (4V+2U, 9.0 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 9.0 CP 186 h
4 V Lecture 56 h
2 U Exercise class (in small groups) 28 h
(4V+2U) 9.0 CP 84 h 186 h

Basedata

SWS 4V+2U
CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. irreg. WiSe
Level [7] Master (Advanced)
Language [EN] English
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-SPAS] Analysis and Stochastics
Livecycle-State [NORM] Active

Notice

The course is offered at least every second winter semester.

Contents

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.

Literature

  • 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.

Materials

Further literature will be announced in the lecture; Exercise material is provided.

Registration

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].

Modules:

Requirements for attendance (formal)

None

References to Course [MAT-64-11-K-7]

Module Name Context
[MAT-64-11A-M-7] Stochastic Differential Equations and Financial Mathematics P: Obligatory 4V+2U, 9.0 LP
[MAT-64-11-M-7] Stochastic Differential Equations P: Obligatory 4V+2U, 9.0 LP