Nagaev, S. V.; Vakhtel’, V. I. On sums of independent random variables without power moments. (Russian, English) Zbl 1224.60099 Sib. Mat. Zh. 49, No. 6, 1369-1380 (2008); translation in Sib. Math. J. 49, No. 6, 1091-1100 (2008). Summary: In [Trans. Am. Math. Soc. 73, 95–107 (1952; Zbl 0047.37502)], D. A. Darling proved the limit theorem for the sums of independent identically distributed random variables without power moments under the functional normalization. We give an alternative proof of Darling’s theorem, using the Laplace transform. Besides, we study the asymptotic behaviour of probabilities of large deviations in the pattern under consideration. Cited in 2 Documents MSC: 60G50 Sums of independent random variables; random walks Keywords:slowly varying function; Laplace transform; binomial distribution; independent random variables; branching processes Citations:Zbl 0047.37502 PDFBibTeX XMLCite \textit{S. V. Nagaev} and \textit{V. I. Vakhtel'}, Sib. Mat. Zh. 49, No. 6, 1369--1380 (2008; Zbl 1224.60099); translation in Sib. Math. J. 49, No. 6, 1091--1100 (2008) Full Text: EuDML EMIS