News
- 25-08-26: First version of the course page online, choodle sent for first meeting (reply asap, latest Friday lunch)
Stochastic partial differential equations (SPDE) are considered in the
sense of Itô. We extend the theory of It̂ stochastic differential
equations to infinite dimensions by considering SPDE in the framework of
Hilbert spaces. This requires the definition of Wiener processes in
Hilbert space and the derivation of the stochastic integral in that
abstract setting. We show existence and uniqueness of mild solutions to
linear SPDE. Mild solutions are then simulated which requires
approximation in space, time, and of the infinite-dimensional driving
Wiener noise. We prove strong and weak convergence rates of the
considered approximation schemes.
The course will start in September and run max until mid-January (LP1-2 2025/26). The schedule will be decided by
the participants at an introductory meeting.
There will be lectures given by the students and an individual project.
The grading scale comprises Fail, (U), Pass (G), and successful completion of the course will be rewarded by 7.5 hp credit points.
XYZday XX/YY XX.XX-YY.YY MVL:XX |
Introduction Discussion of the schedule (Andrea, David, Annika) |
XYZday XX/YY XX.XX-YY.YY MVL:XX |
Preliminaries (LN 1.1, 1.2.2, 1.2.3, 1.2.4) (Who?) |
XYZday XX/YY XX.XX-YY.YY MVL:XX |
Preliminaries (LN 1.1, 1.2.2,
1.2.3, 1.2.4) (Who?) Gaussian measures, Wiener processes (LN 2.1, 2.2) (Who?) |
XYZday XX/YY XX.XX-YY.YY MVL:XX |
Gaussian measures, Wiener
processes (LN 2.1, 2.2) (Who?) |
XYZday XX/YY XX.XX-YY.YY MVL:XX |
Semigroups and approximation (LN
2.4) (Who?) |
XYZday XX/YY XX.XX-YY.YY MVL:XX |
Semigroups and approximation (LN
2.4) (Who?) Stochastic integration, strong and mild solutions (LN 2.3, 2.5.1) (Who?) |
XYZday XX/YY XX.XX-YY.YY MVL:XX |
Stochastic integration, strong
and mild solutions (LN 2.3, 2.5.1) (Who?) |
XYZday XX/YY XX.XX-YY.YY MVL:XX |
Existence, uniqueness, and
properties of solutions (LN 2.5.2, 2.5.3) (Who?) |
XYZday XX/YY XX.XX-YY.YY MVL:XX |
Existence, uniqueness, and properties of solutions (LN 2.5.2,
2.5.3) (Who?) Strong approximation of mild solutions, noise approximation (LN 2.6, 2.7) (Who?) |
XYZday XX/YY XX.XX-YY.YY MVL:XX |
Strong approximation of mild solutions, noise approximation
(LN 2.6, 2.7) (Who?) |
XYZday XX/YY XX.XX-YY.YY MVL:XX |
Weak convergence (Who?) |
XYZday XX/YY XX.XX-YY.YY MVL:XX |
Weak convergence (Who?) (Multilevel) Monte Carlo methods (LN 2.8) (Who?) |
XYZday XX/YY XX.XX-YY.YY MVL:XX |
(Multilevel) Monte Carlo methods (LN 2.8) (Who?) |
XYZday XX/YY XX.XX-YY.YY MVL:XX |
tba and decided |
January 2026? |
Project presentations (tba) |