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 Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2009, Issue 4(70), Pages 52–84 (Mi vsgu241)

Mathematics

About asymptotics and large deviations in the central limit theorem for sums $\sum \mathbf{f(q^nt)}$

L. P. Usol'tsev

Dept. of Probability Theory and Mathematical Statistics, Samara State University, Samara, 443011, Russia

Abstract: In the paper new estimates for the remainder term and large deviations in the central limit theorem for sums $\sum \mathbf{f(q^nt)}$ are obtained. Technique and methods of reasoning contained not only in the classical probability theory, but also in the theory of diophantine equations with exponential function are used in the given proofs.

Keywords: central limit theorem, exponential function, diophantine equation, asymptotics and large deviations.

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UDC: 511.2+519.2
Revised: 14.05.2009

Citation: L. P. Usol'tsev, “About asymptotics and large deviations in the central limit theorem for sums $\sum \mathbf{f(q^nt)}$”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2009, no. 4(70), 52–84

Citation in format AMSBIB
\Bibitem{Uso09} \by L.~P.~Usol'tsev \paper About asymptotics and large deviations in the central limit theorem for sums $\sum \mathbf{f(q^nt)}$ \jour Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya \yr 2009 \issue 4(70) \pages 52--84 \mathnet{http://mi.mathnet.ru/vsgu241}