Mathematical Modelling with Stochastic Partial Differential Equations
Dr. Alexander Kalinin
Schedule and Venue
| Events | Date/Time | Room |
|---|---|---|
| Lectures Dr. Alexander Kalinin | Tuesday, 16:00 - 17:30 Thursday, 8:30 - 10:00 | B 005 |
| Exercise Classes | Wednesday, 16:00 - 17:30 | B 004 |
| Additional Exercise Classes | Thursday, 10:15 - 11:00 | B 046 |
The course will be organised via Moodle. If you want to attend the course, please register in Moodle.
The aim of this course is to give a concise introduction to a class of parabolic stochastic partial differential equations with a particular focus on mathematical modelling. In the first part of the semester, we will deal with Gaussian processes, including fractional Brownian motion and white noise, and consider the Kolmogorov-Chentsov continuity theorem and stochastic integration in a multidimensional setting. In the second part, we will derive unique solutions to such stochastic equations, analyse their path and probabilistic properties and consider relevant applications in mathematical physics.
- Dalang R., Khoshnevisan D., Mueller, C., Nualart, D. and Xiao, Y.: A Minicourse on Stochastic Partial Differential Equations, Springer, 2009.
- Lototsky S. V. and Rozovsky, B. L.: Stochastic Partial Differential Equations, Springer, 2017.
- Röckner, M. and Liu, W.: Stochastic Partial Differential Equations: An Introduction, Springer, 2015.
All three books are available as PDF files for LMU students at the university library.
Target Participants: Master students of Financial and Insurance Mathematics or Mathematics.
Pre-requisites: Probability theory and foundations of stochastic processes in continuous time.
Applicable credits: 9 ECTS. Students may apply the credits from this course to:
- the Master in Financial and Insurance Mathematics, PO 2021 (WP 12).
- the Master in Mathematics, PO 2021 (WP 27).