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K0108-13431bV Specialisation Stochastics B (L)

Instructors: Ph.D. Wojciech Cygan
Event type: Lecture
Org-unit: Faculty of Mathematics
Hours per week: 3
Language of instruction: English
Alternativtitel: Markov Chains
Inhalte: Announcement
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
OPAL-Kurs: https://bildungsportal.sachsen.de/opal/auth/RepositoryEntry/29413441537

Literature

Appointments
Date From To Room Instructors
1 Mon, 12. Apr. 2021 09:20 10:50 Die Veranstaltung findet online statt. Ph.D. Wojciech Cygan
2 Wed, 14. Apr. 2021 13:00 14:30 Die Veranstaltung findet online statt. Ph.D. Wojciech Cygan
3 Mon, 19. Apr. 2021 09:20 10:50 Die Veranstaltung findet online statt. Ph.D. Wojciech Cygan
4 Mon, 26. Apr. 2021 09:20 10:50 Die Veranstaltung findet online statt. Ph.D. Wojciech Cygan
5 Wed, 28. Apr. 2021 13:00 14:30 Die Veranstaltung findet online statt. Ph.D. Wojciech Cygan
6 Mon, 3. May 2021 09:20 10:50 Die Veranstaltung findet online statt. Ph.D. Wojciech Cygan
7 Mon, 10. May 2021 09:20 10:50 Die Veranstaltung findet online statt. Ph.D. Wojciech Cygan
8 Wed, 12. May 2021 13:00 14:30 Die Veranstaltung findet online statt. Ph.D. Wojciech Cygan
9 Mon, 17. May 2021 09:20 10:50 Die Veranstaltung findet online statt. Ph.D. Wojciech Cygan
10 Mon, 31. May 2021 09:20 10:50 Die Veranstaltung findet online statt. Ph.D. Wojciech Cygan
11 Mon, 7. Jun. 2021 09:20 10:50 Die Veranstaltung findet online statt. Ph.D. Wojciech Cygan
12 Wed, 9. Jun. 2021 13:00 14:30 Die Veranstaltung findet online statt. Ph.D. Wojciech Cygan
13 Mon, 14. Jun. 2021 09:20 10:50 Die Veranstaltung findet online statt. Ph.D. Wojciech Cygan
14 Mon, 21. Jun. 2021 09:20 10:50 Die Veranstaltung findet online statt. Ph.D. Wojciech Cygan
15 Wed, 23. Jun. 2021 13:00 14:30 Die Veranstaltung findet online statt. Ph.D. Wojciech Cygan
16 Mon, 28. Jun. 2021 09:20 10:50 Die Veranstaltung findet online statt. Ph.D. Wojciech Cygan
17 Mon, 5. Jul. 2021 09:20 10:50 Die Veranstaltung findet online statt. Ph.D. Wojciech Cygan
18 Wed, 7. Jul. 2021 13:00 14:30 Die Veranstaltung findet online statt. Ph.D. Wojciech Cygan
19 Mon, 12. Jul. 2021 09:20 10:50 Die Veranstaltung findet online statt. Ph.D. Wojciech Cygan
20 Mon, 19. Jul. 2021 09:20 10:50 Die Veranstaltung findet online statt. Ph.D. Wojciech Cygan
21 Wed, 21. Jul. 2021 13:00 14:30 Die Veranstaltung findet online statt. Ph.D. Wojciech Cygan

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Instructors
  • Ph.D. Wojciech Cygan