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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 6, Pages 1369–1380 (Mi smj1925)  
This article is cited in 5 scientific papers (total in 5 papers)

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
Full-text PDF (290 kB) Citations (5)
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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.
Received: 26.05.2004
English version:
Siberian Mathematical Journal, 2008, Volume 49, Issue 6, Pages 1091–1100
DOI: https://doi.org/10.1007/s11202-008-0105-x
Bibliographic databases:
UDC: 519.21
Language: Russian
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
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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