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On sums of independent random variables without power moments

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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.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    S. V. Nagaev

  2. Weierstrass-Institut, Mohrenstrasse, Berlin, Germany

    V. I. Vachtel

Authors
  1. S. V. Nagaev
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  2. V. I. Vachtel
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Corresponding author

Correspondence to S. V. Nagaev.

Additional information

Original Russian Text Copyright © 2008 Nagaev S. V. and Vachtel V. I.

The first author was supported by the Russian Foundation for Basic Research (Grant 02-01-01252); the second author was supported by the Russian Foundation for Basic Research (Grants 02-01-01252 and 02-01-00358) and INTAS (Grant 00-265).

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Novosibirsk; Berlin. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 6, pp. 1369–1380, November–December, 2008.

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Nagaev, S.V., Vachtel, V.I. On sums of independent random variables without power moments. Sib Math J 49, 1091–1100 (2008). https://doi.org/10.1007/s11202-008-0105-x

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  • DOI: https://doi.org/10.1007/s11202-008-0105-x

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