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Course, academic year 2024/2025
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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 2024
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
Guarantor: prof. Lev Klebanov, DrSc.
Teacher(s): prof. Lev Klebanov, DrSc.
Class: M Mgr. PMSE
M Mgr. PMSE > Povinně volitelné
Classification: Mathematics > Probability and Statistics
Is interchangeable with: NSTP157
Annotation -
Limit theorems for convergence to infinitely divisible distributions. Local limit theorems. CLT for stationary sequences of random variables.
Last update: T_KPMS (16.05.2013)
Aim of the course -

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.

Last update: T_KPMS (16.05.2013)
Course completion requirements -

Oral exam.

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

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.

Last update: T_KPMS (16.05.2013)
Teaching methods -

Lecture.

Last update: T_KPMS (04.05.2015)
Requirements to the exam -

Oral exam according to sylabus.

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

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.

Last update: T_KPMS (16.05.2013)
Entry requirements -

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

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