On the strong law of large numbers and the central limit theorem for martingales

Csörgő, Miklós

doi:10.1090/S0002-9947-1968-0221562-X

On the strong law of large numbers and the central limit theorem for martingales
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by Miklós Csörgő PDF

Trans. Amer. Math. Soc. 131 (1968), 259-275 Request permission

Addendum: Trans. Amer. Math. Soc. 136 (1969), 545.

References

F. J. Anscombe, Large-sample theory of sequential estimation, Proc. Cambridge Philos. Soc. 48 (1952), 600–607. MR 51486, DOI 10.1017/s0305004100076386
J. R. Blum, D. L. Hanson, and J. I. Rosenblatt, On the central limit theorem for the sum of a random number of independent random variables, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 1 (1962/63), 389–393. MR 155349, DOI 10.1007/BF00533414
Harald Cramér, Mathematical methods of statistics, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1999. Reprint of the 1946 original. MR 1816288
J. L. Doob, Stochastic processes, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1953. MR 0058896
William Feller, An introduction to probability theory and its applications. Vol. II, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR 0210154
J. Hájek and A. Rényi, Generalization of an inequality of Kolmogorov, Acta Math. Acad. Sci. Hungar. 6 (1955), 281–283 (English, with Russian summary). MR 76207, DOI 10.1007/BF02024392
Michel Loève, Probability theory, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-New York-London, 1960. 2nd ed. MR 0123342
J. Mogyoródi, A central limit theorem for the sum of a random number of independent random variables, Magyar Tud. Akad. Mat. Kutató Int. Közl. 7 (1962), 409–424 (English, with Russian summary). MR 151998
A. Rényi, On mixing sequences of sets, Acta Math. Acad. Sci. Hungar. 9 (1958), 215–228. MR 98161, DOI 10.1007/BF02023873
A. Rényi, On the central limit theorem for the sum of a random number of independent random variables, Acta Math. Acad. Sci. Hungar. 11 (1960), 97–102 (unbound insert) (English, with Russian summary). MR 115204, DOI 10.1007/BF02020627