SubjectsSubjects(version: 873)
Course, academic year 2020/2021
  
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 2020
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: prof. Lev Klebanov, DrSc.
Class: M Mgr. PMSE
M Mgr. PMSE > Povinně volitelné
Classification: Mathematics > Probability and Statistics
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 - Czech
Last update: RNDr. Jitka Zichová, Dr. (23.04.2018)

Složení ústní zkoušky.

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 - Czech
Last update: RNDr. Jitka Zichová, Dr. (18.10.2017)

Zkouška sestává z ústní části. Známka ze zkoušky se stanoví na základě této části. Požadavky u ústní části odpovídají sylabu předmětu v rozsahu, který byl prezentován na přednášce.

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.

 
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