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<p><i>Applying the results of&#xa0;Zaitsev</i> (1987) <i>to specific symmetric distributions with slowly decreasing power tails, we obtained power estimates for the accuracy of the infinitely divisible approximation of the distributions of sums of n i.i.d. random variables of the form</i> <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7980_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="68" /> </InlineMediaObject> <EquationSource Format="TEX">\(O(n^{-1+\varepsilon })\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mo stretchy="false">(</mo> <msup> <mi>n</mi> <mrow> <mo>-</mo> <mn>1</mn> <mo>+</mo> <mi>ε</mi> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> <i>with</i> <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7980_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varepsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> </InlineEquation> <i>arbitrarily close to zero. Bibliography:</i> 41 <i>titles</i>.</p>

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ON THE ACCURACY OF INFINITELY DIVISIBLE APPROXIMATION OF n-FOLD CONVOLUTIONS OF PROBABILITY DISTRIBUTIONS

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Ia. S. Golikova,
  • A. Yu. Zaitsev

摘要

Applying the results of Zaitsev (1987) to specific symmetric distributions with slowly decreasing power tails, we obtained power estimates for the accuracy of the infinitely divisible approximation of the distributions of sums of n i.i.d. random variables of the form \(O(n^{-1+\varepsilon })\) O ( n - 1 + ε ) with \(\varepsilon \) ε arbitrarily close to zero. Bibliography: 41 titles.