On the maximum partial sums of sequences of independent random variables
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- Trans. Amer. Math. Soc. 64 (1948), 205-233 Request permission
Erratum: Trans. Amer. Math. Soc. 64 (1948), 596.
References
- L. Bachelier, Calcul des probabilités, vol. 1, Paris, 1912.
- Harald Bergström, On the central limit theorem in the space $R_k, k>1$, Skand. Aktuarietidskr. 28 (1945), 106–127. MR 15704, DOI 10.1080/03461238.1945.10404921
- Andrew C. Berry, The accuracy of the Gaussian approximation to the sum of independent variates, Trans. Amer. Math. Soc. 49 (1941), 122–136. MR 3498, DOI 10.1090/S0002-9947-1941-0003498-3
- Kai-Lai Chung and Paul Erdös, On the lower limit of sums of independent random variables, Ann. of Math. (2) 48 (1947), 1003–1013. MR 23010, DOI 10.2307/1969391 H. Cramér, Random variables and probability distributions, Cambridge Tracts in Mathematics, No. 36, Cambridge University Press, 1937. —, Sur un nouveau théorème-limite de la théorie des probabilités, Actualités Scientifiques, No. 736, Paris, 1938, pp. 5-23.
- Harald Cramér, Mathematical Methods of Statistics, Princeton Mathematical Series, vol. 9, Princeton University Press, Princeton, N. J., 1946. MR 0016588
- P. Erdös and M. Kac, On certain limit theorems of the theory of probability, Bull. Amer. Math. Soc. 52 (1946), 292–302. MR 15705, DOI 10.1090/S0002-9904-1946-08560-2
- Carl-Gustav Esseen, Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law, Acta Math. 77 (1945), 1–125. MR 14626, DOI 10.1007/BF02392223
- W. Feller, Generalization of a probability limit theorem of Cramér, Trans. Amer. Math. Soc. 54 (1943), 361–372. MR 9262, DOI 10.1090/S0002-9947-1943-0009262-5
- 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
- W. Feller, The fundamental limit theorems in probability, Bull. Amer. Math. Soc. 51 (1945), 800–832. MR 13252, DOI 10.1090/S0002-9904-1945-08448-1 M. Fréchet, Recherches théoriques modernes sur la théorie des probabilités, vol. 1, Paris, 1937. A. Khintchine, Ein Satz der Wahrscheinlichkeitsrechnung, Fund. Math. vol. 6 (1924) pp. 9-10.
- A. Kolmogoroff, Über die Summen durch den Zufall bestimmter unabhängiger Größen, Math. Ann. 99 (1928), no. 1, 309–319 (German). MR 1512451, DOI 10.1007/BF01459098
- A. Kolmogoroff, Über das Gesetz des iterierten Logarithmus, Math. Ann. 101 (1929), no. 1, 126–135 (German). MR 1512520, DOI 10.1007/BF01454828 A. Liapounoff, Nouvelle forme du théorème sur la limite de la probabilité, Mémoires de l’Académie de Saint-Petersbourg (8) vol. 12 (1901). J. V. Uspensky, Introduction to mathematical probability, New York, McGraw-Hill, 1937.
Additional Information
- © Copyright 1948 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 64 (1948), 205-233
- MSC: Primary 60.0X
- DOI: https://doi.org/10.1090/S0002-9947-1948-0026274-0
- MathSciNet review: 0026274