Summary
Kolmogorov's law of the iterated logarithm is extended to the martingale case.
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Chow, Y. S., Robbins, Herbert, Teicher, Henry: Moments of randomly stopped sums. Ann. math. Statistics 36, 789–799 (1965).
Doob, J. L.: Stoachastic processes. New York: Wiley 1953.
Feller, W.: The general form of the so-called law of the iterated logarithm. Trans. Amer. math. Soc. 54, 373–402(1943).
Kolmogorov, A.: über das Gesetz des iterierten Logarithmus. Math. Ann. 101, 126–135 (1929).
Levy, P.: Theorie de l'addition des variables aleatoires 2. Paris: Gauthier-Villars 1954.
Loeve, M.: Probability theory 3. Princeton: Van Nostrand 1963.
Marcinkiewicz, J., Zygmund, A.: Remarque sur la loi du logarithme itere. Fundamenta Math. 29, 215–222 (1937).
Strassen, V.: Almost sure behavior of sums of independent random variables and martingales. Proc. Fifth Berkeley Sympos. math. Statist. Probab. 2, 315–343 (1965).
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This research was supported by National Science Foundation Grant GP 7363.
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Stout, W.F. A martingale analogue of Kolmogorov's law of the iterated logarithm. Z. Wahrscheinlichkeitstheorie verw Gebiete 15, 279–290 (1970). https://doi.org/10.1007/BF00533299
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DOI: https://doi.org/10.1007/BF00533299