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Course, academic year 2016/2017

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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 2014 to 2017
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	Mgr. Michal Kupsa
Class:	M Mgr. PMSE M Mgr. PMSE > Povinně volitelné
Classification:	Mathematics > Probability and Statistics
Incompatibility :	NSTP060
Interchangeability :	NSTP060
Is interchangeable with:	NSTP060

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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.

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)

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

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