Glasnik Matematicki, Vol. 52, No. 2 (2017), 351-360.

THE DAVIS-GUT LAW FOR INDEPENDENT AND IDENTICALLY DISTRIBUTED BANACH SPACE VALUED RANDOM ELEMENTS

Pingyan Chen, Mingyang Zhang and Andrew Rosalsky

Department of Mathematics, Jinan Unversity, Guangzhou, 510630, P. R. China
e-mail: tchenpy@jnu.edu.cn

Department of Mathematics, Jinan Unversity, Guangzhou, 510630, P. R. China
e-mail: zmy1021@qq.com

Department of Statistics, University of Florida, Gainesville, FL 32611, USA
e-mail: rosalsky@stat.ufl.edu


Abstract.   An analog of the Davis-Gut law for a sequence of independent and identically distributed Banach space valued random elements is obtained, which extends the result of Li and Rosalsky (A supplement to the Davis-Gut law. J. Math. Anal. Appl. 330 (2007), 1488-1493).

2010 Mathematics Subject Classification.   60F15.

Key words and phrases.   Davis-Gut law, law of the iterated logarithm, sequence of independent and identically distributed Banach space valued random elements.


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DOI: 10.3336/gm.52.2.11


References:

  1. P.Y. Chen and D.C. Wang, Convergence rates for probabilities of moderate deviations for moving average processes, Acta Math. Sin. (Engl. Ser.) 24 (2008), 611-622.
    MathSciNet     CrossRef

  2. P.Y. Chen and D.C. Wang, Lr convergence for B-valued random elements, Acta Math. Sin. (Engl. Ser.) 28 (2012), 857-868.
    MathSciNet     CrossRef

  3. J.A. Davis, Convergence rates for the law of the iterated logarithm, Ann. Math. Statist. 39 (1968), 1479-1485.
    MathSciNet     CrossRef

  4. U. Einmahl and D. Li, Characterization of LIL behavior in Banach space, Trans. Amer. Math. Soc. 360 (2008), 6677-6693.
    MathSciNet     CrossRef

  5. A. Gut, Convergence rates for probabilities of moderate deviations for sums of random variables with multidimensional indices, Ann. Probab. 8 (1980), 298-313.
    MathSciNet     CrossRef

  6. P. Hartman and A. Wintner, On the law of the iterated logarithm, Amer. J. Math. 63 (1941), 169-176.
    MathSciNet     CrossRef

  7. T.-C. Hu, A. Rosalsky, D. Szynal and A.I. Volodin, On complete convergence for arrays of rowwise independent random elements in Banach spaces, Stochastic Anal. Appl. 17 (1999), 963-992.
    MathSciNet     CrossRef

  8. M. Ledoux and M. Talagrand, Probability in Banach spaces. Isoperimetry and processes, Springer-Verlag, Berlin, 1991.
    MathSciNet     CrossRef

  9. D.L. Li, Convergence rates of law of iterated logarithm for B-valued random variables, Sci. China Ser. A 34 (1991), 395-404.
    MathSciNet    

  10. D. Li and A. Rosalsky, A supplement to the Davis-Gut law, J. Math. Anal. Appl. 330 (2007), 1488-1493.
    MathSciNet     CrossRef

  11. D.L. Li, X. C. Wang and M.B. Rao, Some results on convergence rates for probabilities of moderate deviations for sums of random variables, Internat. J. Math. Math. Sci. 15 (1992), 481-497.
    MathSciNet     CrossRef

  12. X. Liu, H. Qian and L. Cao, The Davis-Gut law for moving average processes, Statist. Probab. Lett. 104 (2015), 1-6.
    MathSciNet     CrossRef

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