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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)
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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)
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Oral exam. Last update: Zichová Jitka, RNDr., Dr. (05.05.2023)
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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)
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Lecture. Last update: T_KPMS (04.05.2015)
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Oral exam according to sylabus. Last update: Zichová Jitka, RNDr., Dr. (05.05.2023)
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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)
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Convergence in distribution, central limit theorem, Fourier transformation of probability measure. Last update: Zichová Jitka, RNDr., Dr. (19.06.2019)
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