Stochastic Differential Equations
Instructor: Dr. Alexander Kalinin
Schedule and Venue
| Events | Date/Time | Room |
|---|---|---|
| Seminar | Wednesday, 16:00 - 17:30 | B041 |
The seminar is conducted by Dr. Alexander Kalinin and administered on Moodle, where interested students are requested to register.
This seminar analyses one-dimensional stochastic differential equations (SDEs) driven by a Brownian motion. Built upon a concise review of semimartingale theory, stochastic integration and Itô's formula, the course establishes the existence and uniqueness of strong solutions under Lipschitz conditions on the drift and diffusion coefficients of the SDE. A special emphasis is placed on affine SDEs, recovering the Brownian bridge, geometric Brownian motion and Ornstein-Uhlenbeck process as explicit solutions.
- Revuz, D. and Yor, M.: Continuous martingales and Brownian motion, Springer-Verlag, 1999.
- Ikeda, N. and Watanabe, S.: Stochastic differential equations and diffusion processes, North-Holland Publishing Co., 1989.
Both books are available as PDF files for LMU students at the university library.
Target Participants: Master students in Mathematics and Financial and Insurance Mathematics.
Pre-requisites: Probability theory and measure and integration theory.
Applicable credits: 3 ECTS. Students may apply the credits from this course to the
- Master in Mathematics, PO 2021 (any seminar module, such as WP 12 or WP 15),
- Master in Financial and Insurance Mathematics, PO 2021 (P 3 or WP 17).