On the strong law of large numbers and the central limit theorem for martingales
HTML articles powered by AMS MathViewer
- 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
Additional Information
- © Copyright 1968 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 131 (1968), 259-275
- MSC: Primary 60.30
- DOI: https://doi.org/10.1090/S0002-9947-1968-0221562-X
- MathSciNet review: 0221562