Ph.D. course on

Stochastic Prtial Differential Equations

LP2 2021/22

Chalmers University of Technology & University of Gothenburg


News

21/10: Preliminary schedule online.

15/10: The first meeting is scheduled for Wednesday, October 20, 11:30 - 12:00 in MVL:15

Teacher

Course coordinator: Annika Lang (annika.lang@chalmers.se)
Teachers: David Cohen and Stig Larsson

Course description

Stochastic partial differential equations (SPDE) are considered in the sense of Itô. We extend the theory of Itô 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 the end of October and run twice a week (4 hours) until mid-January (LP2 2021/22). The schedule will be decided by the participants at an introductory meeting. 

Course literature

Will be updated continuously and still depends on the interest of the audience

Main references

Lecture notes (unsorted)

Books (unsorted)

Schedule

OBS: preliminary schedule. The presentations might start earlier than indicated and the schedule in the last week before Christmas is not finally fixed yet.

Wednesday 20/10
11.30-12.00
MVL:14
Introduction
Discussion of the schedule
(Annika)
Wednesday 10/11
8.15-10
MVL:14
Preliminaries (LN 1.1, 1.2.2, 1.2.3, 1.2.4)
(Per)
Thursday 11/11
10-12
MVL:14
Preliminaries (LN 1.1, 1.2.2, 1.2.3, 1.2.4)
(Per)
Gaussian measures, Wiener processes (LN 2.1, 2.2)
(Kasper)
Wednesday 17/11
8.15-10
MVL:14
Gaussian measures, Wiener processes (LN 2.1, 2.2)
(Kasper)
Thursday 18/11
10-12
MVL:14
Semigroups and approximation (LN 2.4)
(Erik)
Wednesday 24/11
8.15-10
MVL:14
Semigroups and approximation (LN 2.4)
(Erik)
Stochastic integration, strong and mild solutions (LN 2.3, 2.5.1)
(Marcus)
Thursday 25/11
10-12
MVL:14
Stochastic integration, strong and mild solutions (LN 2.3, 2.5.1)
(Marcus)
Wednesday 1/12
8.15-10
MVL:14
Existence, uniqueness, and properties of solutions (LN 2.5.2, 2.5.3)
(Oskar)
Thursday 2/12
10-12
MVL:14
Existence, uniqueness, and properties of solutions (LN 2.5.2, 2.5.3)
(Oskar)
Strong approximation of mild solutions, noise approximation (LN 2.6, 2.7)
(Johan)
Wednesday 8/12
8.15-10
MVL:14
Strong approximation of mild solutions, noise approximation (LN 2.6, 2.7)
(Johan)
Thursday 9/12
10-12
MVL:14
Weak convergence
(Jan)
Wednesday 15/12
8.15-10
MVL:14
Weak convergence
(Jan)
(Multilevel) Monte Carlo methods (LN 2.8)
(Ioanna)
Thursday 16/12
10-12
MVL:14
(Multilevel) Monte Carlo methods (LN 2.8)
(Ioanna)
Wednesday 22/12
8.15-10
MVL:14
tba and decided
January 2022
Project presentations (tba)

Examination

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.

Mailing list

If you want to receive information on the course by email, please contact annika.lang@chalmers.se