Computational Stochastics Group

Registration for oral examinations

Dear students,

these are the days for the oral examination offered by Mr. Ritter:

  • 15. September 2021
  • 20. October 2021.

Please contact Mrs. Höffler via Email (hoeffler(at)mathematik.uni-kl.de )to schedule an appointment and indicate your

  • Name,
  • matriculation number,
  • department/course of studies (if not mathematics),
  • examiner,
  • examination subject,
  • preferred day of examination.

Mrs. Höffler enters your dates into the examination administration system and sends you the examination agreement via E-Mail. Please sign it and send it back via E-mail to Mrs. Höffler.

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.

Bachelor

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Master

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Lectures offered in winter term 2021/2022

The following lectures are offered by our working group in winter term 2021/2022.

High-Dimensional Integration

Contents

  • discrepancy of point sets and quasi-Monte Carlo methods
  • lattice rules
  • sparse grids and Smolyak formulas
  • anisotropic Korobov and Sobolev spaces on finite- and infinite-dimensional domains
  • lower error bounds and complexity of continuous problems
  • randomization
  • the probabilistic method

Instructor

Material

Probability Theory

Contents

  • Types of convergence
  • Characteristic functions
  • Markov kernels
  • Sums of independent random variables
  • Strong laws of large numbers, variants of the central limit theorem
  • Conditional expectation
  • Martingales in discrete time
  • Brownian motion

Instructor

Lectures offered in winter term 2020/2021

The following lectures were offered during winter term 2020/2021 by our working group:

Introduction to Functional Analysis (in German)

Contents

  • Banach spaces: examples, bounded linear operators, compactness
  • Hilbert spaces: bounded linear operators, Lax-Milgram theorem, spectral theory

Infos, Material

Stochastic Differential Equations

Contents

  • 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

Infos, Material

Lectures offered in summer term 2020

The following lectures were offered during summer term 2020 by our working group:

Fundamentals of Mathematics II

Instructor

Infos, Material

Dates

Lectures:

  • (room 52-207, 11:45 - 13:15) tuesdays
  • (room 24-102, 11:45 - 13:15) thursdays
  • (room 46-215, 10:00 - 11:30)
    fridays

 

Monte-Carlo-Algorithmen

Dates

Tuesday,  15:30 - 17:05

Thursday, 15:30 - 17:00

Room 31-302

 

 

Lectures offered in winter term 2019/20

The following lectures were 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

 

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

 

Lectures offered in summer term

The 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

 

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