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Abstract <p>This paper examines the expansion of the strictly stable law for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(x \to 0\)</EquationSource> <!--RusMath2570086Saenko-m1--> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(x \to \infty \)</EquationSource> <!--RusMath2570086Saenko-m2--> </InlineEquation> in the case of extreme values of the asymmetry parameter. Asymptotic expansions of the probability density and distribution functions are obtained, as are estimates of the residual terms of these expansions. Based on the estimates of the residual terms, a criterion is presented that makes it possible to determine the coordinate region within which it is possible to use these asymptotic expansions. The calculations confirm the validity of the expressions.</p>

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Estimation of the Remainder Term in the Expansion of the Stable Law for Extreme Values of the Asymmetry Parameter

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • V. V. Saenko

摘要

Abstract

This paper examines the expansion of the strictly stable law for \(x \to 0\) and \(x \to \infty \) in the case of extreme values of the asymmetry parameter. Asymptotic expansions of the probability density and distribution functions are obtained, as are estimates of the residual terms of these expansions. Based on the estimates of the residual terms, a criterion is presented that makes it possible to determine the coordinate region within which it is possible to use these asymptotic expansions. The calculations confirm the validity of the expressions.