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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
DOI: https://doi.org/10.1090/S0002-9939-1973-0329007-3
MathSciNet review: 0329007
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Abstract | References | Similar Articles | Additional Information

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, https://doi.org/10.1214/aoms/1177700166
  • [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
  • [3] F. Jonas, Unpublished Thesis, Erlangen, 1967.
  • [4] A. V. Skorohod, \cyr Issledovaniya po teorii sluchaĭnykh protsessov (Stokhasticheskie differentsial′nye uravneniya i predel′nye teoremy dlya protsessov Markova), Izdat. Kiev. Univ., Kiev, 1961 (Russian). MR 0185619
    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
  • [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
  • [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, https://doi.org/10.1007/BF00534910
  • [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: https://doi.org/10.1090/S0002-9939-1973-0329007-3
Keywords: Iterated logarithm, Brownian motion, martingale difference, representation theorem, stationary ergodic
Article copyright: © Copyright 1973 American Mathematical Society