A specialization in Computational Stochastics is based on a number of core courses, primarily from Analysis and Stochastics, which are outlined below. Prospective Bachelor students may also want to look at an elementary introduction (in German) to Computational Stochastics.
Lectures offered in winter term 2019/20
Following lectures are offered during winter term 2019 /20 by our working group:
Fundamentals of Mathematics I
High-dimensional Integration (Seminar)
We study the following two papers:
Mendelson, Pajor: On singular values of matrices with independent rows (2006)
Krieg, Ullrich: On L_2-approximation in Hilbert spaces using function values (2019)
Tuesday, 13:45 - 15:15
Preliminary Meeting on October 9th, at 14:30, in Room 31-251.
Lectures offered in summer term
Following lectures were offered during summer term 2019 by our working group:
Algorithms and complexities of high- and infinite-dimensional integration problems. We study, in particular,
- discrepancy of point sets and quasi-Monte Carlo methods,
- the curse of dimensionality,
- lower bounds and complexity of continuous problems.
Lectures (room 31-302, 10:00 - 11:30) on thursdays
Exercises (room 31-215, 17:00 - 18:30) on tuesdays, bi-weekly
(first meeting April 30th, second meeting May 14th)
The exercise class on July 9th will be shifted to July 16th.
For further information see: KIS
Monte Carlo Algorithms
Monte Carlo algorithms are algorithms that use random numbers. The lecture provides an introduction to this important basic technique from mathematics and computer science. We study, in particular,
- direct simulation
- simulation of distributions and stochastic processes
- variance reduction
- high-dimensional integration
as well as applications from physics, finance, and actuarial mathematics.
Lectures are being held on tuesdays and thursdays, 13:45 - 15:15 in room 31-302 IBZ.
First lecture starts Tuesday, 16.04.2019.
Exercises are being held on fridays, 13:45 - 15:15 in room 31-302 IBZ.
First exercise starts Friday, 26.04.2019.
For further information see KIS
Lectures in winter term
Following lectures were offered during winter term 2018 / 2019 by our working group:
Stochastic Differential Equations
- Brownian motion
- Continuous-time martingales
- Stochastic integration
- Strong and weak solutions of SDEs
- Stochastic representation of solutions of PDEs
- Ito-Taylor schemes
- Stochastic multi-level algorithms
Lectures (room 31-302, 15:30 - 17:00) tuesdays and thursdays
Exercises (room 31-302, 17:05 - 18:35) thursdays
For further information please see: [KIS]
Die Vorlesung gibt eine Einführung in die Stochastik (Wahrscheinlichkeitstheorie, Simulation, Statistik), ohne Kenntnisse der Maß- und Integrationstheorie vorauszusetzen.
The first lecture starts on Tuesday, 23.10.2018, 11:45 - 13:15, room 48-208.
For further information please see KIS