Sharp estimates of the convergence rate of distributions of normed sums to the normal law

A combination of the method of coupling, Stein technique and the quasi-convex analysis allowed author to derive unimprovable inequalities characterizing the distance between a probability distribution and its zero bias transformation in terms of a wide class of minimal metrics. In the presentation the basic ideas of the mentioned approach are explained. Moreover, it is shown how to obtain optimal estimates of the convergence rate in the Lyapunov central limit theorem when using ideal probability metrics.
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