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