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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 4, Pages 837–854 (Mi smj1882)  

This article is cited in 6 scientific papers (total in 6 papers)

An integro-local theorem applicable on the whole half-axis to the sums of random variables with regularly varying distributions

A. A. Mogul'skii

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (373 kB) Citations (6)
References:
Abstract: We obtain an integro-local limit theorem for the sum $S(n)=\xi(1)+\cdots+\xi(n)$ of independent identically distributed random variables with distribution whose right tail varies regularly; i.e., it has the form $\mathbf P(\xi\ge t)=t^{-\beta}L(t)$ with $\beta>2$ and some slowly varying function $L(t)$. The theorem describes the asymptotic behavior on the whole positive half-axis of the probabilities
$$ \mathbf P(S(n)\in[x,x+\Delta)) $$
as $x\to\infty$ for a fixed $\Delta>0$; i.e., in the domain where the normal approximation applies, in the domain where $S(n)$ is approximated by the distribution of its maximum term, as well as at the “junction” of these two domains.
Keywords: regularly varying distribution, integro-local theorem, integral theorem, theorem applicable on the whole half-axis, function of deviations, large deviations, domain of normal approximation, domain of maximum term approximation.
Received: 16.01.2007
Revised: 14.05.2007
English version:
Siberian Mathematical Journal, 2008, Volume 49, Issue 4, Pages 669–683
DOI: https://doi.org/10.1007/s11202-008-0064-2
Bibliographic databases:
UDC: 519.21
Language: Russian
Citation: A. A. Mogul'skii, “An integro-local theorem applicable on the whole half-axis to the sums of random variables with regularly varying distributions”, Sibirsk. Mat. Zh., 49:4 (2008), 837–854; Siberian Math. J., 49:4 (2008), 669–683
Citation in format AMSBIB
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  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
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