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Course, academic year 2022/2023
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Entropy in Probability Dynamical Systems - NMTP569
Title: Entropie v pravděpodobnostních dynamických systémech
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: Mgr. Michal Kupsa
Class: M Mgr. PMSE
M Mgr. PMSE > Povinně volitelné
Classification: Mathematics > Probability and Statistics
Is interchangeable with: NSTP060
Annotation -
Last update: T_KPMS (16.05.2013)
The basic elements of ergodic theory are presented. We mainly focus on entropy and recurrence. Tight relationship between ergodic theory and the theory of finite-states stationary processes will be presented.
Aim of the course -
Last update: T_KPMS (16.05.2013)

To present the broadly used notion of entropy in the frame of the ergodic theory.

Course completion requirements -
Last update: RNDr. Jitka Zichová, Dr. (29.10.2019)

Oral exam.

Literature - Czech
Last update: T_KPMS (16.05.2013)

K. Petersen: Ergodic Theory, Cambridge Univ. Press, 1983

P. Shields: The Ergodic Theory of Discrete Sample Path, Graduate Studies in Mathematics, AMS, 1996

Teaching methods -
Last update: T_KPMS (16.05.2013)


Requirements to the exam -
Last update: RNDr. Jitka Zichová, Dr. (29.10.2019)

According to the sylabus and the content of the lecture.

Syllabus -
Last update: T_KPMS (16.05.2013)

1. Probability (measure-theoretical) dynamical systems, finite-states stationary processes - definitions, examples, ergodicity, isomorfismus of probability dynamical systems, factorization

2. Entropy of the process, entropy of the system, strictly positive entropy - Kolmogorov property

3. Kolmogorov-Sinai theorem on generators, Shannon-McMillan-Breimann theorem

4. Recurrence, Ornstein-Weiss theorem, Lempel-Ziv algorithm for data compression

Entry requirements -
Last update: RNDr. Jitka Zichová, Dr. (05.06.2019)

Basics of mathematical analysis, measure tehory, Lebesgue integral. Basics of probability theory and linear algebra.

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