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Vorlesung + Übung: Stochastische Prozesse (Stochastik IV) - Details
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General information

Course name Vorlesung + Übung: Stochastische Prozesse (Stochastik IV)
Subtitle Stochastic Processes
Course number MTH-1670
Semester SS 2024
Current number of participants 23
Home institute Stochastik und ihre Anwendungen
participating institutes Institut für Mathematik
Courses type Vorlesung + Übung in category Teaching
Next date Wednesday, 17.04.2024 08:15 - 09:45, Room: (1008/L)
Pre-requisites Good knowledge of measure-theoretic probability theory (e.g. bachelor modules "Stochastik I/II"). Basics might be recalled from the first chapters of Bovier's lecture notes (reference below).
Online/Digitale Veranstaltung Veranstaltung wird in Präsenz abgehalten.
Hauptunterrichtssprache englisch
Literaturhinweise Anton Bovier: Stochastic Processes, Lecture Notes, University of Bonn, 2022
www.dropbox.com/s/5f6s9fnpf4gejgf/wt2-new.pdf

James R. Norris: Markov Chains, Cambridge University Press, 2009

Peter Mörters, Yuval Peres: Brownian Motion, Cambridge University Press, 2010
www.mi.uni-koeln.de/~moerters/book/book.pdf

Lecture notes will be written along the course, updates available under "Dateien"
Miscellanea Overview (plan):
1. What is a stochastic process?
2. Discrete-time Markov processes
3. Martingales
4. Continuous-time Markov chains
5. Diffusion processes
ECTS points 9

Rooms and times

(Raum 2004/L)
Monday: 10:00 - 11:30, weekly (12x)
(1008/L)
Wednesday: 08:15 - 09:45, weekly (13x)
Friday: 08:15 - 09:45, weekly (14x)

Fields of study

Module assignments

Comment/Description

Welcome to the course Stochastic Processes!
The course provides an introduction to the theory of stochastic processes, including discrete-time Markov processes, martingales, continuous-time Markov chains and diffusion processes. We will use several constructions of continuous-time Markov processes including generators and martingale problems, and show how different processes are related via scaling limits. The exercises will mostly focus on applications and models of time-dependent phenomena with randomness.