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Modul
Introduction to Stochastic Differential Equations [M-MATH-106045]
Credits
4Recurrence
UnregelmäßigDuration
1 SemesterLanguage
EnglishLevel
4Version
1Responsible
Organisation
- KIT-Fakultät für Mathematik
Part of
Bricks
Identifier | Name | LP |
---|---|---|
T-MATH-112234 | Introduction to Stochastic Differential Equations | 4 |
Competence Certificate
The module will be completed with an oral exam (approx. 30 min).
Competence Goal
The students will
- know fundamental examples for linear and non-linear stochastic differential equations,
- be able to apply basic solution concepts for stochastic differential equations,
- know fundamental theorems of stochastic calculus and will be able to apply these to stochastic differential equations.
Prerequisites
none
Content
- Introduction and recapitulation of stochastic integration, Itô's formula, Lévy Theorem
- Burkholder-Davis-Gundy inequality
- Existence and uniqueness of solutions of stochastic differential equations
- Explicit solutions of linear stochastic differential equations
- Change of the time scale of Brownian motion
- Representation of continuous time martingales
- Brownian martingales
- Local and global solutions of stochastic differential equations
- Girsanov Theorem
Recommendation
The contents of the course "Probability Theory" are strongly recommended. The contents of the course "Continuous Time Finance" are recommended.
Workload
Total workload: 120 hours
Attendance: 45 hours
- lectures, problem classes, and examination
Self-studies: 75 hours
- follow-up and deepening of the course content,
- work on problem sheets,
- literature study and internet research relating to the course content,
- preparation for the module examination