## 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