Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-64-11-M-7

Stochastic Differential Equations (M, 9.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-64-11-M-7 Stochastic Differential Equations 9.0 CP (270 h)

Basedata

CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. irreg. WiSe
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
Lecturers of the department Mathematics
Area of study [MAT-SPAS] Analysis and Stochastics
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Notice

This module cannot be used together with the module [MAT-61-11-M-7] Financial Mathematics because of large content overlaps. It is part of the module [MAT-64-11A-M-7] Stochastic Differential Equations and Financial Mathematics.

The module is offered at least every second winter semester.

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V+2U MAT-64-11-K-7
Stochastic Differential Equations
P 84 h 186 h - - PL1 9.0 irreg. WiSe
  • About [MAT-64-11-K-7]: Title: "Stochastic Differential Equations"; Presence-Time: 84 h; Self-Study: 186 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 86415 ("Stochastic Differential Equations")

Evaluation of grades

The grade of the module examination is also the module grade.


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.

Competencies / intended learning achievements

Upon successful completion of this module, the students have acquired advanced knowledge in the analysis of stochastic differential equations. Moreover, they have gained insights into the modelling and numerical handling of SDEs. They are able to name and to prove the essential propositions of the lecture as well as to classify and to explain the connections.

By completing the given exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. In addition, they have learnt how to apply these techniques to new problems, analyze them and develop solution strategies.

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.

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 Module / Module Number [MAT-64-11-M-7]

Module-Pool Name
[MAT-70-MPOOL-7] Specialisation Stochastic Analysis (M.Sc.)
[MAT-81-MPOOL-7] Specialisation Partial Differential Equations (M.Sc.)
[MAT-8x-MPOOL-7] Specialisation Modelling and Scientific Computing (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)
[MAT-RM-MPOOL-7] Pure Mathematics (Advanced Modules M.Sc.)