Dr. Wojciech Cygan

© privat

Name

Dr. Wojciech Cygan

Wissenschaftlicher Mitarbeiter

Send Email

Send encrypted mail via the SecureMail portal (for TUD external users only).

Organization Name

Institute of Mathematical Stochastics

Institute of Mathematical Stochastics

Address work

Visitor Address:

Willersbau, C 235 Zellescher Weg 12-14

01069 Dresden

Show map of this location.

work Tel.

+49 351 463-34276

fax Fax

+49 351 463-37251

wojciech.cygan@​tu-dresden.de

Forschungsgebiete:

• Wahrscheinlichkeitstheorie und stochastische Prozesse
• Potentialtheorie
• Markov Prozesse, Dirichlet forms, Isoperimetrische Ungleichungen, usw.

Meine Publikationsliste und die Vorträge finden Sie auf meiner Homepage

Lehrveranstaltungen im Sommersemester 2021:

• Vorlesung und Übung: Vertiefung Stochastik (Modul Math Ba STOCHV, Sprache: Englisch). The lecture offers a rigorous introduction to the theory of Markov Chains. Loosely speaking, a Markov chain is a stochastic process in discrete time which enjoys a useful property of forgetting the past. It means that our knowledge about the possible future evolution of the process is determined solely by its behaviour at the present moment of time, and not by its behaviour in the past.  Markov chains serve as handy tools while modelling real life phenomena such as weather forecasting, gambling, stock prices prediction, simulation of chemical processes, structure-analysis of signals in information theory, webpages rankings, and many others. The main goal of the lecture is to provide a solid theoretical background which will be accompanied by a series of stimulating examples. A brief Outline: Introduction: basic definitions and examples, Classification of states, Recurrence vs Transience, Ergodic theorems, Reversible Markov chains, Population-growth models, Elements of the potential theory of Markov chains. 

  Problem Sessions

  Each two weeks (on Wednesday) there will be an online problem session where we will discuss exercises and examples related to the lecture. Students will be encouraged to present their own ideas and solutions. 

  Prerequisites

  You should be familiar with basic concepts of the probability theory, in particular you should know and understand conditional expectation and conditional probability: a comprehensive guide is Chapter VII of the book Measure, Integral, Probability, & Processes by René Schilling. Helpful (but not a must) would be an elementary knowledge of generating functions in spirit of complex analysis.                                         More information soon in OPAL.

• Übung zur Vorlesung Analysis (Mathematik II) für Wirtschaftswissenschaftler und Verkehrswirtschaftler
  Vorlesender: Prof. Dr. Dietmar Ferger
  Alle Informationen dazu finden Sie im OPAL