Ph.D. course

Stochastic Partial Differential Equations

News

  • 25-08-26: First version of the course page online, choodle sent for first meeting (reply asap, latest Friday lunch)

When and where?

  • Course code: NFMV019 (GU master MMF500) with registration via FUBAS
  • LP1-2 2025/26 (old course pages 2021 and 2017)
  • Schedule: tba
  • Place: tba

Who?

  • Department of Mathematical Sciences, Chalmers University of Technology & University of Gothenburg
  • Teachers: David Cohen, Annika Lang (examiner), and Andrea Papini
  • Place: tba

Course description

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.


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.


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



  • OBS: preliminary old schedule. The presentations might start earlier than indicated.
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)