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 Sibirsk. Mat. Zh., 2008, Volume 49, Number 6, Pages 1369–1380 (Mi smj1925)

On sums of independent random variables without power moments

S. V. Nagaeva, V. I. Vakhtel'b

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Weierstrass Institute for Applied Analysis and Stochastics

Abstract: In 1952 Darling proved the limit theorem for the sums of independent identically distributed random variables without power moments under the functional normalization. This paper contains an alternative proof of Darling?s theorem, using the Laplace transform. Moreover, the asymptotic behavior of probabilities of large deviations is studied in the pattern under consideration.

Keywords: slowly varying function, Laplace transform, binomial distribution, independent random variables, branching processes.

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English version:
Siberian Mathematical Journal, 2008, 49:6, 1091–1100

Bibliographic databases:

UDC: 519.21

Citation: S. V. Nagaev, V. I. Vakhtel', “On sums of independent random variables without power moments”, Sibirsk. Mat. Zh., 49:6 (2008), 1369–1380; Siberian Math. J., 49:6 (2008), 1091–1100

Citation in format AMSBIB
\Bibitem{NagVak08} \by S.~V.~Nagaev, V.~I.~Vakhtel' \paper On sums of independent random variables without power moments \jour Sibirsk. Mat. Zh. \yr 2008 \vol 49 \issue 6 \pages 1369--1380 \mathnet{http://mi.mathnet.ru/smj1925} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2499107} \transl \jour Siberian Math. J. \yr 2008 \vol 49 \issue 6 \pages 1091--1100 \crossref{https://doi.org/10.1007/s11202-008-0105-x} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000261792400014} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-57749190590} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. S. V. Nagaev, “The renewal theorem without further power moments”, Theory Probab. Appl., 56:1 (2012), 166–175
2. Khartov A.A., “Asymptotic Analysis of Average Case Approximation Complexity of Hilbert Space Valued Random Elements”, J. Complex., 31:6 (2015), 835–866
3. Alexander K.S., Berger Q., “Local Limit Theorems and Renewal Theory With No Moments”, Electron. J. Probab., 21 (2016), 66
4. Caravenna F., Sun R., Zygouras N., “the Dickman Subordinator, Renewal Theorems, and Disordered Systems”, Electron. J. Probab., 24 (2019), 101
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