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Sibirsk. Mat. Zh., 2008, Volume 49, Number 5, Pages 1007–1018 (Mi smj1898)  

This article is cited in 1 scientific paper (total in 1 paper)

Tauberian and Abelian theorems for rapidly decaying distributions and their applications to stable laws

A. A. Borovkov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We establish some assertions of Tauberian and Abelian types which enable us to find connections between the asymptotic properties of the Laplace transform at infinity and the asymptotics of the corresponding densities of rapidly decaying distributions (at infinity or in some neighborhood of zero). As applications of our Tauberian type theorems we present asymptotics for the density $f^{(\alpha,\rho)}(x)$ of “extreme” stable laws with parameters $(\alpha,\rho)$ for $\rho=\pm1$ and $x$ lying in the domain of rapid decay of $f^{(\alpha,\rho)}(x)$. This asymptotics had been found in [1–5] by a more complicated method.

Keywords: Tauberian theorems, Abelian theorems, rapidly decaying distribution, Cramér transform, density asymptotics.

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English version:
Siberian Mathematical Journal, 2008, 49:5, 796–805

Bibliographic databases:

UDC: 519.21
Received: 26.10.2007

Citation: A. A. Borovkov, “Tauberian and Abelian theorems for rapidly decaying distributions and their applications to stable laws”, Sibirsk. Mat. Zh., 49:5 (2008), 1007–1018; Siberian Math. J., 49:5 (2008), 796–805

Citation in format AMSBIB
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\by A.~A.~Borovkov
\paper Tauberian and Abelian theorems for rapidly decaying distributions and their applications to stable laws
\jour Sibirsk. Mat. Zh.
\yr 2008
\vol 49
\issue 5
\pages 1007--1018
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\transl
\jour Siberian Math. J.
\yr 2008
\vol 49
\issue 5
\pages 796--805
\crossref{https://doi.org/10.1007/s11202-008-0078-9}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. Deligiannidis, S. A. Utev, “Asymptotic variance of the self-intersections of stable random walks using Darboux–Wiener theory”, Siberian Math. J., 52:4 (2011), 639–650  mathnet  crossref  mathscinet  isi
  • Сибирский математический журнал Siberian Mathematical Journal
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