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Journal of Mathematical Sciences

, Volume 93, Issue 3, pp 336–340 | Cite as

Approximation of convolutions by accompanying laws under the existence of moments of low orders

  • A. Yu. Zaitsev
Article

Abstract

It is shown that if a one-dimensional distribution F has finite moment of order 1+β for some β, 1/2≤β≤1, then the rate of approximation of the n-fold convolution Fn by accompanying laws is O(n−1/2). Futhermore, if Eξ2 = ∞ and 1/2<β<1, then the rate of approximation is o(n−1/2). The question about the true rate of approximation of Fn by infinitely divisible and accompanying laws is discussed. Bibliography: 27 titles.

Keywords

Convolution True Rate Finite Moment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Kluwer Academic/Plenum Publishers 1999

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  • A. Yu. Zaitsev

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