Registration for oral examinations
Dear students,
these are the days for the oral examination offered by Prof. Dr. Ritter:
- 22. February 2024
- 14. March 2024
- 04. April 2024
Please see Mrs. Höffler, building 31, room 451 to schedule an appointment.
Fachpraktikum
We will offer a 'Fachpraktikum' on Gaussian RBF Kernels in SS 2024. See here for further infos.
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.
Lectures offered in summer term 2024
The following lectures are offered by our working group in summer term 2024.
Fundamentals of Mathematics I
Instructor
Dates
- Tuesday, 10:00 - 11:30 (room 48-210)
- Thursday, 10:00 - 11:30 (room 48-210)
- Friday, 11:45 - 13:15 (room 48-210)
Reading Courses, Seminars and Proseminars
Proseminar "Quasi-Monte-Carlo-Methoden"
Instructor: Klaus Ritter
Dates to be announced
Lectures offered in winter term 2023/2024
The following lectures were offered by our working group in winter term 2023/2024.
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
Dates
Lectures (room 31-302)
Tuesday, 11:45 - 13:15
Thursday 10:00 - 11:30
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
Dates
Lectures:
Tuesday, 15:30 - 17:00, Room 48-208
Thursday, 15:30 - 17:00, Room 48-208
Exercises:
Wednesday, 11:45h - 13:15, Room 36-265
Friday, 10:00h - 11:30, Room 41-243
Lectures offered in summer term 2023
The following lectures were offered by our working group in summer term 2023.
Funktionalanalysis
Contents
Satz von Hahn-Banach und Anwendungen; Baire'scher Kategorien Satz und Anwendungen (Prinzip der gleichmäßigen Beschränktheit, Satz von Banach-Steinhaus, Satz von der offenen Abbildung, Satz von der inversen Abbildung, Satz vom abgeschlossenen Graphen); schwache Konvergenz (Satz von Banach-Alaoglu, reflexive Banach-Räume, Lemma von Mazur und Anwendungen), Projektionen (Satz vom abgeschlossenen Komplement); beschränkte Operatoren (adjungierte Operatoren, Spektrum, Resolvente, normale Operatoren); kompakte Operatoren (Fredholm-Operatoren, Fredholm-Alternative und Anwendungen, Spektralsatz (Riesz-Schauder) und Anwendungen auf normale Operatoren).
Dates
Lectures:
Wednesday, 11:45 - 13:15, Room 48-210
Friday, 10:00 - 11:30, Room 48-208
Exercises:
Friday, 11:45h - 13:15, Room 48-538
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.
Instructor
Ritter
Infos, Material
Dates
Lectures are being held in room 31-302
Tuesdays, 15:30 - 17:00
Thursdays, 15:30 - 17:00
Lectures are being held in room 31-302
Thursdays, 10:00 - 11:30
Lectures offered in winter term 2022/2023
The following lectures are offered by our working group in winter term 2022/2023.
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
Dates
Monday, 13:45 - 15:15
Tuesday, 13:45 - 15:15
Thursday, 15:30 - 17:00
Room 31-302
Stochastische Methoden
Contents
Die Vorlesung gibt eine Einführung in die Stochastik (Wahrscheinlichkeitstheorie, Simulation, Statistik), ohne Kenntnisse der Maß- und Integrationstheorie vorauszusetzen.
Dates
Lectures:
Tuesday, 11:45 - 13:15
Friday, 11:45 - 13:15
Room 48-208
Exercises:
Wednesday, 13:45h - 15:15, Room 48-210
Thursday, 10:00h - 11:30, Room 48-210
Friday, 08:15h - 09:45, Room 48-538
Friday, 10:00h - 11:30, Room 46-267
Reading Courses, Seminars and Proseminars
Seminar "Interpolation of Hilbert Spaces"
Instructor: Ritter
Dates to be announced
Lectures offered in summer term 2022
The following lectures were offered by our working group in summer term 2022.
Measure and Integration Theory
Contents
- systems of sets and measurable mappings
- Caratheodory's Theorem
- the k-dimensional Lebesgue measure
- construction and properties of integral w.r.t. a measure
- L^p-spaces
- product spaces
Dates
Lectures are being held in room 48-208
Thursday 08:00 - 09:30
Exercises are being held every two weeks in room
48-538, Thursday 12:00 - 13:30
44-465, Friday 08:00 - 09:30
48-538, Friday 14:00-15:30
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.
Instructor
Infos, Materials
Dates
Lectures are being held in room 31-302
Tuesdays, 16:00 - 17:30
Thursdays, 16:00 - 17:30
Time and room for the exercises will be announced.
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
Dates
Lectures (room 31-302)
Monday, 14:00 - 15:30
Thursday 10:00 - 11:30
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
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)
Stochastic Differential Equations
Lectures offered in summer term 2020
The following lectures were offered during summer term 2020 by our working group:
Fundamentals of Mathematics II
Instructor
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
Instructor
Infos, Material
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
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.
Instructor
Infos, Material
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