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Proceedings of the American Mathematical Society
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A note on Strassen's version of the law of the iterated logarithm


Author: A. K. Basu
Journal: Proc. Amer. Math. Soc. 41 (1973), 596-601
MSC: Primary 60F15; Secondary 60G45
MathSciNet review: 0329007
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Abstract: Strassen's law of the iterated logarithm is extended to stationary ergodic martingales and to a non-identically-distributed case.


References [Enhancements On Off] (What's this?)

  • [1] Y. S. Chow, Local convergence of martingales and the law of large numbers, Ann. Math. Statist. 36 (1965), 552–558. MR 0182040 (31 #6264)
  • [2] V. F. Gapoškin, The law of the iterated logarithm for Abel’s and Cesàro’s methods of summation, Teor. Verojatnost. i Primenen 10 (1965), 449–459 (Russian, with English summary). MR 0195133 (33 #3336)
  • [3] F. Jonas, Unpublished Thesis, Erlangen, 1967.
  • [4] A. V. Skorokhod, Studies in the theory of random processes, Translated from the Russian by Scripta Technica, Inc, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965. MR 0185620 (32 #3082b)
  • [5] Olaf P. Stackelberg, On the law of the iterated logarithm. I. II, Nederl. Akad. Wetensch. Proc. Ser. A 67 = Indag. Math. 26 (1964), 48–55, 56–67. MR 0161351 (28 #4558)
  • [6] V. Strassen, An invariance principle for the law of the iterated logarithm, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 3 (1964), 211–226 (1964). MR 0175194 (30 #5379)
  • [7] W. F. Stout, The Hartman-Wintner law of the iterated logarithm for martingales, Ann. Math. Statist. 41 (1970), 2158-2160.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0329007-3
PII: S 0002-9939(1973)0329007-3
Keywords: Iterated logarithm, Brownian motion, martingale difference, representation theorem, stationary ergodic
Article copyright: © Copyright 1973 American Mathematical Society