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On the estimate of the rate of convergence in the law of iterated logarithm

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Probability Theory and Mathematical Statistics

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References

  1. Darling D.A., Robbins H. Iterated logarithm inequalities. Proc.Nat.Acad.Sci.USA. 1967, 57, 1188–1192.

    Article  MathSciNet  MATH  Google Scholar 

  2. Robbins H., Siegmund D. Iterated logarithm and related statistical procedures. Math of the Design Sci. 2-Lectures in Appl.Math., Amer.Math.Soc., 1968,267–279.

    Google Scholar 

  3. Strassen V.K. Almost sure behavior of sum of independent variables and martingales.Proc. 5th Berkeley Symp.Math.Stat.Prob., 1967, v.2, part I, 315–343.

    MathSciNet  Google Scholar 

  4. Komlos J., Mayor P., Tusnady G., An approximation of partial sums of independent RV-s and sample DF. Z.Wahr.verw.Geb., 1975, 32, I/2, 111–133.

    Article  MATH  Google Scholar 

  5. Chow Y.S., Lai T.L., Some one-sided theorems on the tail distribution of sample sums with applications to the last time and largest excess of boundary crossing. Trans.Amer.Math.Soc., 1975, 208, 51–72.

    Article  MathSciNet  MATH  Google Scholar 

  6. Lai T.L., Boundary crossing probabilities for sample sums and confidence sequences. Ann.Math.Stat., 1976, 4, 2, 299–312.

    MATH  Google Scholar 

  7. Lai T.L., Lan K.K., On the last time the numbers and the number of the boundary crossing related to the law of large numbers and the law of the iterated logarithm., Z.Warh.verw.Geb., 1976, 34, I, 59–71.

    Article  MathSciNet  MATH  Google Scholar 

  8. Gafurov M.U., Slastnikov A.D., On the distribution of the last exit time, the excess and the number of exits of a random walk beyong a curved boundary, Sov.Math.Docl., 1981, 23, 2, 285–288.

    MATH  Google Scholar 

  9. Gafurov M.U., Estimates for the probabilistic characteristics of a random walk over curved boundary. Doct.diss.Tashkent, 1981.

    Google Scholar 

  10. Davis J.A., Convergence rates for the law of the iterated logarithm, Ann. Math.Stat., 1968, 39, 5, 1479–1485.

    MATH  Google Scholar 

  11. Petrov V.V., Sums of independent random variables. Moscow, "Nauka", 1973.

    Google Scholar 

  12. Gafurov M.U., Siragdinov S.H., Some generalizations of results Erdos-Katz related with the law large numbers, and its applications. Kibernetica, 1979, 15, 4, 272–292.

    MATH  Google Scholar 

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© 1983 Springer-Verlag Berlin Heidelberg

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Gafurov, M.U. (1983). On the estimate of the rate of convergence in the law of iterated logarithm. In: Prokhorov, J.V., Itô, K. (eds) Probability Theory and Mathematical Statistics. Lecture Notes in Mathematics, vol 1021. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072910

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  • DOI: https://doi.org/10.1007/BFb0072910

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12718-5

  • Online ISBN: 978-3-540-38701-5

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