Content:

This seminar is at the interface of  stochastic differential equations and numerical analysis. The seminar will be held as a block course. In the first four weeks there will be four lectures explaining basics of the topics specified bellow. At the beginning of the semester, students will be given papers with particular methods related to those topics that they should work on and implement by the end of the semester. In the last weeks of the semester,  students will  give presentations in which the project results will be presented and they will also submit short report about their topic.

The seminar will cover a selection from the following topics:

• Full discretization of parabolic PDEs
• Numerical methods for SDEs, such as Euler-Maruyama Method, Milstein Method, exponential integrators
• Weak and strong convergence
• Galerkin methods for semilinear stochastic PDEs
• Monte-Carlo and Multilevel Monte-Carlo sampling methods

Target audience: 

M.Sc. Mathematik/Physik, BMS course

Requirements:

Stochastic I and Numerics II.  Basic knowledge from measure theory, functional analysis and numerical analysis.

Suggested reading:

[1] T. J. Sullivan. Introduction to Uncertainty Quantification, volume 63 of Texts in Applied Mathematics. Springer, 2015.

[2] Lord, Gabriel J., Catherine E. Powell, and Tony Shardlow. An Introduction to computational stochastic PDEs. Vol. 50. Cambridge University Press, 2014.

[3]  P. E. Kloeden, E. Platen. Numerical Solution of Stochastic Differential Equations. Springer 1992

[4] V. Thomee. Galerkin Finite Element Methods for Parabolic Problems. Springer 2006