Convergence rates in the law of large numbers

Authors:
Leonard E. Baum and Melvin Katz

Journal:
Trans. Amer. Math. Soc. **120** (1965), 108-123

MSC:
Primary 60.30

MathSciNet review:
0198524

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**[1]**Leonard E. Baum and Melvin Katz,*Convergence rates in the law of large numbers*, Bull. Amer. Math. Soc.**69**(1963), 771–772. MR**0156373**, 10.1090/S0002-9904-1963-11027-7**[2]**Leonard E. Baum, Melvin Katz, and Robert R. Read,*Exponential convergence rates for the law of large numbers*, Trans. Amer. Math. Soc.**102**(1962), 187–199. MR**0133855**, 10.1090/S0002-9947-1962-0133855-X**[3]**P. Erdös,*On a theorem of Hsu and Robbins*, Ann. Math. Statistics**20**(1949), 286–291. MR**0030714****[4]**Carl-Gustav Esseen,*Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law*, Acta Math.**77**(1945), 1–125. MR**0014626****[5]**W. Feller,*The general form of the so-called law of the iterated logarithm*, Trans. Amer. Math. Soc.**54**(1943), 373–402. MR**0009263**, 10.1090/S0002-9947-1943-0009263-7**[6]**Melvin L. Katz,*The probability in the tail of a distribution*, Ann. Math. Statist.**34**(1963), 312–318. MR**0144369****[7]**Melvin L. Katz,*Note on the Berry-Esseen theorem*, Ann. Math. Statist.**34**(1963), 1107–1108. MR**0151996****[8]**Michel Loève,*Probability theory*, 2nd ed. The University Series in Higher Mathematics. D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-New York-London, 1960. MR**0123342****[9]**Frank Spitzer,*A combinatorial lemma and its application to probability theory*, Trans. Amer. Math. Soc.**82**(1956), 323–339. MR**0079851**, 10.1090/S0002-9947-1956-0079851-X

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DOI:
http://dx.doi.org/10.1090/S0002-9947-1965-0198524-1

Article copyright:
© Copyright 1965
American Mathematical Society