Ph.D. course on

Stochastic Partial Differential Equations

LP2 2017/18

Chalmers University of Technology & University of Gothenburg

News

26/10: The preliminary schedule is online. The goal is that less than 2 lectures are required per topic. Students have to be prepared to present earlier.
17/10: The first meeting is scheduled for Thursday, October 26, 10:00 in MVL:15

Teacher

Course coordinator: Annika Lang
Email: annika.lang@chalmers.se
Office: MVL2086

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 2017/18). 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

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.

Thursday 26/10
10-11
MVL:15
 Introduction
Discussion of the schedule
(Annika)
Monday 6/11
8.30-10
MVL:15
 Preliminaries (LN 1.1, 1.2.2, 1.2.3, 1.2.4)
(Christoffer)
Tuesday 7/11
10-12
MVL:15
 Preliminaries (LN 1.1, 1.2.2, 1.2.3, 1.2.4)
(Christoffer)
Monday 13/11
8.30-10
MVL:15 		Gaussian measures, Wiener processes (LN 2.1, 2.2)
(Hanna)
Tuesday 14/11
10-12
MVL:15 		Gaussian measures, Wiener processes (LN 2.1, 2.2)
(Hanna)
Monday 20/11
8.30-10
MVL:15 		Semigroups and approximation (LN 2.4)
(Milo)
Tuesday 21/11
10-12
MVL:15 		Semigroups and approximation (LN 2.4)
(Milo)
Tuesday 28/11
10-12
MVL:15 		Stochastic integration, strong and mild solutions (LN 2.3, 2.5.1)
(Anders)
Wednesday 29/11
8.30-10
MVL:15
 Stochastic integration, strong and mild solutions (LN 2.3, 2.5.1)
(Anders)
Monday 4/12
8.30-10
MVL:15 		Existence, uniqueness, and properties of solutions (LN 2.5.2, 2.5.3)
(Helga)
Tuesday 5/12
10-12
MVL:15 		Existence, uniqueness, and properties of solutions (LN 2.5.2, 2.5.3)
(Helga)
Strong approximation of mild solutions, noise approximation (LN 2.6, 2.7)
(Christian)
Friday 8/12
10-12
MVL:15		 Strong approximation of mild solutions, noise approximation (LN 2.6, 2.7)
(Christian)
Monday 11/12
8.30-10
MVL:15 		Strong approximation of mild solutions, noise approximation (LN 2.6, 2.7)
(Christian)
(Multilevel) Monte Carlo methods (LN 2.8)
(Yuguan)
Tuesday 12/12
10-12
MVL:15 		(Multilevel) Monte Carlo methods (LN 2.8)
(Yuguan)
Wednesday 10/1
10-12
MVL:15
 Project presentation 1
around week 4 Project presentation 2

Examination

There will be exercises, an individual project, presentations, and lectures given by the students. 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