#### 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

21/10: Preliminary schedule online.

15/10: The first meeting is scheduled for Wednesday, October 20, 11:30 - 12:00 in MVL:15Teachers: David Cohen and Stig Larsson

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.

Main references

#### Schedule

#### Examination

There will be lectures given by the students and an individual project

- Barth and Lang: Lecture notes (LN) distributed to the participants
- Kovács, Larsson, Lindgren: Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise
- Debussche and Printems: Weak order for the discretization of the stochastic heat equation
- Wang: Weak error estimates of the exponential Euler scheme for semi-linear SPDEs without Malliavin calculus

Lecture notes (unsorted)

- Levajkovic and Cohen: SPDEs: From Theory to Implementation distributed to the participants
- Kovács and Larsson: Introduction to stochastic partial differential equations
- Bréhier: A short introduction to Stochastic PDEs
- Hao Shen: Lecture Notes on Math 833 – Stochastic PDEs (Draft) (first chapters)
- Jentzen: Stochastic Partial Differential Equations: Analysis and Numerical Approximations
- Punshon-Smith: An introduction to SPDE: Lecture Notes
- Hairer: An Introduction to Stochastic PDEs
- Balan: A gentle introduction to SPDEs: the random field approach
- Khoshnevisan: Stochastic Integration and Stochastic Partial Differential Equations: a Tutorial
- Sanz-Solé: An Introductory Course on Stochastic Partial Differential Equations
- Pardoux: Stochastic Partial Differential Equations
- Tim Jaschek: Probability meets PDEs: The Numerics of Stochastic Heat Equation

Books (unsorted)

- Prévôt and Röckner: A Concise Course on Stochastic Partial Differential Equations
- Liu and Röckner: Stochastic Partial Differential Equations: An Introduction
- Da Prato and Zabczyk: Stochastic Equations in Infinite Dimensions
- Peszat and Zabczyk: Stochastic Partial Differential Equations with Lévy Noise. An Evolution Equation Approach
- Lord, Powell, and Shardlow: An Introduction to Computational Stochastic PDEs (last chapters)
- Kruse: Strong and Weak Approximation of Semilinear Stochastic Evolution Equations
- Walsh: An introduction to stochastic partial differential equations

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) |

. 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