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Asymptotic expansions for derivatives of stable laws

Identifieur interne : 000A75 ( Istex/Corpus ); précédent : 000A74; suivant : 000A76

Asymptotic expansions for derivatives of stable laws

Auteurs : M. Wiessner

Source :

RBID : ISTEX:C9B06AAFC348CCB9F557CD13CCAC02B64BEA8E7A

Abstract

Abstract: For the derivativesp (k)(x; α, γ) of the stable density of index α asymptotic formulae (of Plancherel Rotach type) are computed ask→∞ thereby exhibiting the detailed analytic structure for large orders of derivatives. Generalizing known results for the special case of the one-sided stable laws (O<α<1, γ=-α) the whole range for the index of stability and the asymmetry parameter γ is covered.

Url:
DOI: 10.1007/BF02352693

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ISTEX:C9B06AAFC348CCB9F557CD13CCAC02B64BEA8E7A

Le document en format XML

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<ArticleTitle Language="En">Asymptotic expansions for derivatives of stable laws</ArticleTitle>
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<GivenName>M.</GivenName>
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<OrgName>Universität Trier</OrgName>
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<Postbox>Postfach 3825</Postbox>
<Postcode>D-5500</Postcode>
<City>Trier</City>
<Country>W.-Germany</Country>
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<Heading>Abstract</Heading>
<Para>For the derivatives
<Emphasis Type="Italic">p</Emphasis>
<Superscript>(k)</Superscript>
(x; α, γ) of the stable density of index α asymptotic formulae (of Plancherel Rotach type) are computed as
<Emphasis Type="Italic">k</Emphasis>
→∞ thereby exhibiting the detailed analytic structure for large orders of derivatives. Generalizing known results for the special case of the one-sided stable laws (
<Emphasis Type="Italic">O</Emphasis>
<α<1, γ=-α) the whole range for the index of stability and the asymmetry parameter γ is covered.</Para>
</Abstract>
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<Heading>AMS 1980 subject classifications</Heading>
<Keyword>60E07</Keyword>
<Keyword>60E10</Keyword>
<Keyword>33A65</Keyword>
<Keyword>33A70</Keyword>
</KeywordGroup>
<KeywordGroup Language="En">
<Heading>Key words and phrases</Heading>
<Keyword>Stable laws</Keyword>
<Keyword>derivatives</Keyword>
<Keyword>asymptotic expansions</Keyword>
<Keyword>saddle point method</Keyword>
<Keyword>formulae of Plancherel-Rotach type</Keyword>
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<SimplePara>This paper contains the main results of a thesis accepted by the Fachbereich IV der Universität Trier.</SimplePara>
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<abstract lang="en">Abstract: For the derivativesp (k)(x; α, γ) of the stable density of index α asymptotic formulae (of Plancherel Rotach type) are computed ask→∞ thereby exhibiting the detailed analytic structure for large orders of derivatives. Generalizing known results for the special case of the one-sided stable laws (O<α<1, γ=-α) the whole range for the index of stability and the asymmetry parameter γ is covered.</abstract>
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<title>Periodica Mathematica Hungarica</title>
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<titleInfo type="abbreviated">
<title>Period Math Hung</title>
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<dateIssued encoding="w3cdtf">1990-12-01</dateIssued>
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<subject>
<genre>Mathematics</genre>
<topic>Mathematics, general</topic>
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