Computational Stochastics Group


General Information

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.

Important Links

  • KIS: Dates and lectures
  • URM: Registration for exercises (open until 18. April 2019)
  • OpenOLAT: Material and further information

Lectures offered in winter term 2019/20

Following lectures are offered during winter term 2019 /20 by our working group:

Fundamentals of Mathematics I

Instructor

Infos, Material

Dates

Lectures:

  • (room 46-210, 10:00 - 11:30) tuesdays
  • (room 46-220, 10:00 - 11:30) thursdays
  • (room 46-210, 10:00 - 11:30) fridays

The first lecture starts on Tuesday, 29.10.

For further information please see  [KIS]

 

 

High-dimensional Integration (Seminar)

Contents

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)

Instructor

Klaus Ritter

Date

Tuesday, 13:45 - 15:15

Room 31-302

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:

High-Dimensional Integration

Contents

Algorithms and complexities of high- and infinite-dimensional integration problems. We study, in particular,

  • discrepancy of point sets and quasi-Monte Carlo methods,
  • randomization
  • the curse of dimensionality,
  • lower bounds and complexity of continuous problems.

Instructor

Infos, Material

Date

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

Contents

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.

Date

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

Content

  • 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

Material

Date

Regular time:

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]

 

 

Stochastische Methoden

Content

Die Vorlesung gibt eine Einführung in die Stochastik (Wahrscheinlichkeitstheorie, Simulation, Statistik), ohne Kenntnisse der Maß- und Integrationstheorie vorauszusetzen.

Team

 Ritter, Hefter, Stroot,
Eisenhuth, Gräfensteiner, Hofmann

Material

Date

The first lecture starts on Tuesday, 23.10.2018, 11:45 - 13:15, room 48-208.

For further information please see KIS

 

 

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