Exact and asymptotically exact constants in the Berry - Esseen inequality, its refinements and generalizations. Part I

1. Calculation of the exact values of numerical constants in convergence rate estimation in the central limit theorem: sport or science?
2. History of the absolute constant in classical Berry-Esseen`s inequality estimation problem. The Esseen constant.
3. Method of solving the problem. Smoothing inequalities. Conditional estimators of the absolute constant in the Berry-Esseen inequality.
4. The Berry-Esseen inequality with refined structure.
5. The analogues of the classical Berry-Esseen inequality for Poisson random sums with constant whitch is less than the Esseens constant.
The second part of the lecture will take place at the Big Seminar of Probability department on November 18.