Lithuanian Mathematical Journal

, Volume 29, Issue 4, pp 333–338 | Cite as

Lower bound for the rate of convergence in the CLT in a Hilbert space

  • M. Bloznelis
Article

Keywords

Hilbert Space 

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Literature Cited

  1. 1.
    V. V. Sazonov, Normal Approximation-Some Recent Advances, Springer-Verlag, Berlin-Heidelberg-New York (1981).Google Scholar
  2. 2.
    V. V. Senatov, “Uniform estimates of the rate of convergence in the multidimensional central limit theorem,” Teor. Veroyatn. Primen.,25, No. 4, 757–770 (1980).Google Scholar
  3. 3.
    S. T. Rachev and J. E. Yukich, “Rates for the CLT via new ideal metrics,” Preprint (1988).Google Scholar
  4. 4.
    M. M. Bloznyalis, “A remark on the rate of convergence of absolute moments in the multidimensional CLT in the case of a stable limit distribution,” in: Abstracts of Report, 29th Conference of the Lithuanian Mathematical Society [in Russian], Vilnius State University (VGU), Vilnius (1988), pp. 19–20.Google Scholar
  5. 5.
    J. Kuelbs and V. Mandrekar, “Domains of attraction of stable measures on a Hilbert space,” Stud. Mathematica,1, 149–162 (1974).Google Scholar
  6. 6.
    V. I. Paulauskas and A. Yu. Rachkauskas, Precision of Approximation in the Central Limit Theorem in Banach Spaces [in Russian], Mokslas, Vilnius (1987).Google Scholar
  7. 7.
    V. Yu. Bentkus, “Lower estimates of the rate of convergence in the central limit theorem in Banach spaces,” Liet. Mat. Rinkinys,25, No. 4, 10–21 (1985).Google Scholar
  8. 8.
    V. V. Sazonov, “On the multidimensional central limit theorem,” Sankhya, Ser. A,30, 181–204 (1968).Google Scholar
  9. 9.
    V. M. Zolotarev, Current Theory of Summation of Independent Random Variables [in Russian], Nauka, Moscow (1986).Google Scholar
  10. 10.
    J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces. I, Springer-Verlag, Berlin-Heidelberg-New York (1977).Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

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  • M. Bloznelis

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