Subjects

Your browser does not support JavaScript, or its support is disabled. Some features may not be available.

Limit Theorems for Sums of Random Variables - NMTP537

Title:	Limitní věty pro součty náhodných veličin
Guaranteed by:	Department of Probability and Mathematical Statistics (32-KPMS)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2022
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter 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:	prof. Lev Klebanov, DrSc.
Class:	M Mgr. PMSE M Mgr. PMSE > Povinně volitelné
Classification:	Mathematics > Probability and Statistics
Is interchangeable with:	NSTP157

Opinion survey results Examination dates WS schedule Noticeboard

Annotation -

Last update: T_KPMS (16.05.2013)

Limit theorems for convergence to infinitely divisible distributions. Local limit theorems. CLT for stationary sequences of random variables.

Aim of the course -

Last update: T_KPMS (16.05.2013)

Limit theorems for the sums of random variables.

There are given the limit theorems for the sums of a random and nonrandom number of random variables.

Course completion requirements -

Last update: RNDr. Jitka Zichová, Dr. (05.05.2023)

Oral exam.

Literature - Czech

Last update: T_KPMS (16.05.2013)

Ibragimov I.A., Linnik Y.V.: Independent and Stationary Dependent Random Variables. Moscow, Nauka,1965.

Samorodnitsky G., Taqu, M.: Stable Non-Gaussian Random Processes. Chapman&Hall, New York, 1994.

Klebanov, L.: Heavy - tailed Distributions. Matfyzpress, Praha, 2003.

Teaching methods -

Last update: T_KPMS (04.05.2015)

Lecture.

Requirements to the exam -

Last update: RNDr. Jitka Zichová, Dr. (05.05.2023)

Oral exam according to sylabus.

Syllabus -

Last update: T_KPMS (16.05.2013)

1. Probability distributions and characteristic functions. 2. Infinitely divisible distrubutions. 3. General limit theoremd for convergence to infinitely divisible distributions. 4. Central limit theorem and asymptotic expansions in it. 5. Local limit theorems. 6. Probability of large deviations. 7. Stationary sequences of random variables. Mixing conditions. 8. Central limit theorem for stationary sequences of random variables.

Reference books: Literatura: Petrov V.V.: Sums of Independent random variables in russian), Nauka, Moskva 1965.

Ibragimov I.A., Linnik Y.V.: Independent and Stationary Dependent Random Variables (in russian), Nauka, Moskva 1965.

Entry requirements -

Last update: RNDr. Jitka Zichová, Dr. (19.06.2019)

Convergence in distribution, central limit theorem, Fourier transformation of probability measure.