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On the order law of the iterated logarithm


Author: I. K. Matsak
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 68 (2003).
Journal: Theor. Probability and Math. Statist. 68 (2004), 93-101
MSC (2000): Primary 60B12
DOI: https://doi.org/10.1090/S0094-9000-04-00598-8
Published electronically: May 24, 2004
MathSciNet review: 2000398
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Abstract | References | Similar Articles | Additional Information

Abstract: We study the classical laws of the iterated logarithm due to Kolmogorov and Hartman-Wintner for random variables assuming values in Banach lattices.


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  • 1. V. V. Petrov, Sums of Independent Random Variables, ``Nauka", Moscow, 1972; English transl., Springer-Verlag, Berlin, 1975. MR 48:1288
  • 2. N. H. Bingham, Variants of the law of the iterated logarithm, Bull. London Math. Soc. 18 (1986), 433-467. MR 87k:60087
  • 3. M. Ledoux and M. Talagrand, Probability in Banach Spaces, Springer-Verlag, Berlin, 1991. MR 93c:60001
  • 4. J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete 92, A Series of Modern Surveys in Mathematics, vol. 2, Springer-Verlag, Berlin, 1979. MR 58:17766
  • 5. L. V. Kantorovich and G. P. Akilov, Functional Analysis in Normed Spaces, Fizmatgiz, Moscow, 1959; English transl., Mcmillan, New York, 1964. MR 22:9837
  • 6. K. Yosida, Functional Analysis, Springer-Verlag, Berlin, 1965. MR 31:5054
  • 7. I. K. Matsak Mean $\psi$-deviation of a random element in a Banach lattice and its applications, Teor. Veroyatnost. i Mat. Statist. 60 (1999), 129-141; English transl. in Theory Probab. Math. Statist. 60 (2000), 137-149.
  • 8. -, On the law of the iterated logarithm in Banach lattices, Teor. Veroyatnost. i Primenen. 44 (1999), no. 4, 865-874; English transl. in Theory Probab. Appl. 44 (2000), no. 4. MR 2003a:60008
  • 9. M. Weiss, On the law of the iterated logarithm, J. Math. Mech. 8 (1959), 121-132. MR 21:1639
  • 10. A. I. Martikainen, On the one-sided law of the iterated logarithm, Teor. Veroyatnost. i Primenen. 30 (1985), no. 4, 694-705; English transl. in Theory Probab. Appl. 30 (1986), no. 4. MR 87a:60038
  • 11. W. Feller An Introduction to Probability Theory and Its Applications, vol. 2, Wiley, New York, 1971. MR 42:5292
  • 12. S. A. Chobanyan and V. I. Tarieladze, A counterexample concerning the CLT in Banach spaces, Lect. Notes Math. 656 (1978), 25-30. MR 80d:60015
  • 13. I. K. Matsak and A. N. Plichko, Central limit theorem in a Banach space, Ukrain. Mat. Zh. 40 (1988), no. 2, 234-239; English transl. in Ukrainian Math. J. 40 (1989). MR 89g:60015
  • 14. S. A. Rakov, On Banach spaces for which an Orlicz theorem does not hold, Mat. Zametki 14 (1973), 101-106; English transl. in Math. Notes 14 (1974). MR 48:9373
  • 15. N. N. Vakhania, V. I. Tarieladze, and S. A. Chobanyan, Probability Distributions on banach Spaces, ``Nauka", Moscow, 1985; English transl., Kluwer, Dordrecht, 1987. MR 86j:60014
  • 16. V. A. Egorov, On the law of the iterated logarithm, Teor. Veroyatnost. i Primenen. 14 (1969), no. 4, 722-729; English transl. in Theory Probab. Appl. 14 (1970), no. 4. MR 42:1193

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Additional Information

I. K. Matsak
Affiliation: Kyiv State University for Technology and Design, Nemirovich-Danchenko Street 2, Kyiv 02011, Ukraine

DOI: https://doi.org/10.1090/S0094-9000-04-00598-8
Received by editor(s): September 1, 2000
Published electronically: May 24, 2004
Article copyright: © Copyright 2004 American Mathematical Society

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