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Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.]:
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Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.], 2009, Issue 12, Pages 77–86 (Mi vtpmk323)  

Probabilistic models

On nonuniform estimates of the remainder terms of the Bergstrem-Chebyshev asymptotic expansions

A. V. Syulyukin

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A nonuniform estimate of the remainder term of the one-term Bergstrom-Chebyshev asymptotic expansion for the density of the sum of independent identically distributed random variables is obtained. It is shown that such estimates can be obtained for the Bergstrom-Chebyshev expansions of arbitrary length.

Keywords: central limit theorem, asymptotic expansions, the accuracy of approximation, nonuniform estimates.

UDC: 519.214
Received: 12.01.2009
Revised: 25.02.2009

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