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

This article is cited in 4 scientific papers (total in 4 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

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.

Full text: PDF file (290 kB)
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English version:
Siberian Mathematical Journal, 2008, 49:6, 1091–1100

Bibliographic databases:

UDC: 519.21
Received: 26.05.2004

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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\paper On sums of independent random variables without power moments
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\vol 49
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\pages 1369--1380
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\pages 1091--1100
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\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
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    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Khartov A.A., “Asymptotic Analysis of Average Case Approximation Complexity of Hilbert Space Valued Random Elements”, J. Complex., 31:6 (2015), 835–866  crossref  mathscinet  zmath  isi  elib  scopus
    3. Alexander K.S., Berger Q., “Local Limit Theorems and Renewal Theory With No Moments”, Electron. J. Probab., 21 (2016), 66  crossref  mathscinet  zmath  isi  scopus
    4. Caravenna F., Sun R., Zygouras N., “the Dickman Subordinator, Renewal Theorems, and Disordered Systems”, Electron. J. Probab., 24 (2019), 101  crossref  mathscinet  zmath  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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