Abstract:
In the paper, estimates of the convergence rate in the central limit theorem are obtained. The estimates take into account large deviations and closeness of summands' distributions to the normal one. In the paper we prove two lemmas on the convergence rate for the compositions of certain $k$-dimensional Borel measures satisfying Cramer's condition.
Citation:
S. Ya. Šorgin, “Non-classical estimates of the rate of convergence in the central limit theorem which take into account large deviations”, Teor. Veroyatnost. i Primenen., 27:2 (1982), 308–318; Theory Probab. Appl., 27:2 (1983), 324–337
\Bibitem{Sho82}
\by S.~Ya.~{\v S}orgin
\paper Non-classical estimates of the rate of convergence in the central limit theorem which take into account large deviations
\jour Teor. Veroyatnost. i Primenen.
\yr 1982
\vol 27
\issue 2
\pages 308--318
\mathnet{http://mi.mathnet.ru/tvp2352}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=657925}
\zmath{https://zbmath.org/?q=an:0565.60018}
\transl
\jour Theory Probab. Appl.
\yr 1983
\vol 27
\issue 2
\pages 324--337
\crossref{https://doi.org/10.1137/1127034}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1983QN71900010}
Linking options:
https://www.mathnet.ru/eng/tvp2352
https://www.mathnet.ru/eng/tvp/v27/i2/p308
This publication is cited in the following 4 articles:
L. Saulis, V. Statulevičius, Limit Theorems of Probability Theory, 2000, 185
S. V. Nagaev, “Probabilistic inequalities for sums of independent random variables in terms of truncated pseudomoments”, Theory Probab. Appl., 42:3 (1998), 520–528
M. U. Gafurov, V. I. Rotar', “On the exit of random walk out of the curvilinear domain”, Theory Probab. Appl., 28:1 (1984), 179–184
V. I. Rotar', “On summation of independent variables in a non-classical situation”, Russian Math. Surveys, 37:6 (1982), 151–175