On strong bounds for sums of independent random variables which tend to a stable distribution

On strong bounds for sums of independent random variables which tend to a stable distribution
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Trans. Amer. Math. Soc. 81 (1956), 135-154

DOI: https://doi.org/10.1090/S0002-9947-1956-0077015-7

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References

W. Doeblin, Sur l’ensemble de puissances d’une loi de probabilité, Studia Math. 9 (1940), 71–96 (French, with Ukrainian summary). MR 5541, DOI 10.4064/sm-9-1-71-96

On the magnitude of the error in the approach to stable distributions

William Feller, Fluctuation theory of recurrent events, Trans. Amer. Math. Soc. 67 (1949), 98–119. MR 32114, DOI 10.1090/S0002-9947-1949-0032114-7
W. Feller, A limit theorem for random variables with infinite moments, Amer. J. Math. 68 (1946), 257–262. MR 16569, DOI 10.2307/2371837

Quelques théorèmes de la théorie des probabilités

Sur les séries dont les termes sont des variables éventuelles indépendantes

K. L. Chung and G. A. Hunt, On the zeros of $\sum ^n_1\pm 1$, Ann. of Math. (2) 50 (1949), 385–400. MR 29488, DOI 10.2307/1969462
Miriam Lipschutz, On strong laws for certain types of events connected with sums of independent random variables, Ann. of Math. (2) 57 (1953), 318–330. MR 56225, DOI 10.2307/1969862
W. Feller, The general form of the so-called law of the iterated logarithm, Trans. Amer. Math. Soc. 54 (1943), 373–402. MR 9263, DOI 10.1090/S0002-9947-1943-0009263-7
K. L. Chung and P. Erdös, On the application of the Borel-Cantelli lemma, Trans. Amer. Math. Soc. 72 (1952), 179–186. MR 45327, DOI 10.1090/S0002-9947-1952-0045327-5