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Stochastical Analysis
(dt. Stochastische Analysis)

Level, degree of commitment Specialization module, compulsory elective module
Forms of teaching and learning,
workload
Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements
9 CP
Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination (individual examination)
Language,
Grading
English,
The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Business Mathematics.
Duration,
frequency
One semester,
Regularly alternating with other specialization modules
Person in charge of the module's outline Prof. Dr. Hajo Holzmann

Contents

We introduce stochastic integration and applications. Different topics cover, for instance, stochastic differential equations, jump processes and applications in financial mathematics.


Qualification Goals

The students

  • Have gained an insight into the research field of stochastic analysis,
  • know basic structures and techniques of stochastic analysis,
  • know selected applications of stochastic analysis,
  • have deepened mathematical working methods (developing mathematical intuition and its formal justification, abstraction, proof),
  • have improved their oral communication skills in exercises by practicing free speech in front of an audience and in discussion.

Prerequisites

None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis, Probability Theory.


Applicability

Module imported from M.Sc. Business Mathematics.

It can be attended at FB12 in study program(s)

  • B.Sc. Mathematics
  • B.Sc. Business Mathematics
  • M.Sc. Data Science
  • M.Sc. Computer Science
  • M.Sc. Mathematics
  • M.Sc. Business Mathematics
  • LAaG Mathematics

When studying M.Sc. Computer Science, this module can be attended in the study area Profile Area Mathematics.


Recommended Reading

  • Oksendal, B., „Stochastic Differential Equations: An Introduction with Applications“. Springer-Verlag Berlin 1998
  • Karatzas, I., Shreve, S., „Brownian Motion and Stochastic Calculus“. Springer-Verlag Berlin 1991
  • Protter, P., „Stochastic Integration and Differential Equations: A New Approach“. Springer-Verlag Berlin 2003
  • Revuz, D., Yor, M., „Continuous Martingales and Brownian Motion“. Springer 2005



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2023/24. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.