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Probability Theory on Vector Spaces II pp 234–243Cite as

The rates of convergence in the central limit theorem in Banach spaces

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 828))

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References

  1. V. Bernotas "On closeness of distributions of two sums of independent random variables with values in some Banach spaces". Liet.matem.rink. 18, 4 (1978), p. 5–12 (in Russian) English translation in "Transaction of Lithuanian Math.Soc."

    MathSciNet  MATH  Google Scholar 

  2. V. Bernotas "An estimate of closeness of two distributions of normed sums of random variables with values in some Banach spaces". Liet.matem.rink. 19, 3 (1979), p. 194–196 (In Russian)

    Google Scholar 

  3. V. Bernotas, V. Paulauskaus "Non-uniform estimate in the Central Limit Theorem in some Banach spaces". Liet.matem.rink. 19, 2 (1979) p. 25–45 (in Russian)

    Google Scholar 

  4. Yu.V.Borovskih, A.Račkauskas "Asymptotics of distributions in the Banach spaces". Liet.matem.rink. 19, 4 (1979), (in Russian)

    Google Scholar 

  5. R.N. Bhattacharya, R. Rao "Normal approximation and asymptotic expansions, John Willey and Sons, N.Y. 1976

    MATH  Google Scholar 

  6. P.L. Butzer, L. Hahn "General Theorems on Ratse of Convergence of Distribution of Random variables I, II. Jour. of Multivariate Anal. 8, 2 (1978) 181–220.

    Article  MathSciNet  MATH  Google Scholar 

  7. A.Cartan, Differential calculus, Moscov 1971 (Russian translation)

    Google Scholar 

  8. V.J. Čebotarev "On the estimates of the rate of convergence in the central limit theorem in lp" Dokl.Akad.Nauk SSSR, 247, 2 (1979), 301–303 (in Russian)

    MathSciNet  Google Scholar 

  9. E. Gine "Bounds for the speed of convergence in the central limit theorem in C(S). Z.Wahrscheinlichkeits. Verw.Geb. 36 (1976) 317–331

    Article  MathSciNet  MATH  Google Scholar 

  10. N.P. Kandelaki "On a limit theorem in Hilbert space, Trans.of Computer Center of AN.GSSR; 5, 1 (1965)46–55 (in Russian)

    Google Scholar 

  11. J. Kuelbs, T. Kurtz "Berry — Eseen estimates in Hilbert space and on application to the law of the iterated logarithm", Ann.Probab. 2, 3(1974) 387–407

    Article  MathSciNet  MATH  Google Scholar 

  12. S.V.Nagajev, V.J.Čebotarev, "Estimates of the rate of convergence in the central limit theorem in l2 in the case of independent coordinates, Abstracts of communications, second Vilnius conf. on probab. and math.stat., 1977, 68–69 (in Russian)

    Google Scholar 

  13. S.V.Nagajev, V.J.Čebotarev "On the rate of convergence in the central limit theorem for l2-valued random variables", in book "Mathematical analysis and related problems of mathematics" Novosibirsk, "Nayka", 1978, p.153–182

    Google Scholar 

  14. V. Paulauskas "On the closeness of distributions of sums of independent random variables with values in Hilbert space". Liet.matem.rink., 15, 3 (1975) 177–200, (in Russian)

    MathSciNet  MATH  Google Scholar 

  15. V. Paulauskas "On convergence of some functionals of sums of independence random variables in a Banach space", Liet. matem.rink. 16, 3 (1976) 103–121 (in Russian)

    MathSciNet  MATH  Google Scholar 

  16. V. Paulauskas "On the rate of convergence in the central limit theorem in some Banach spaces", Teor.verojat.i primen. 21, 4 (1976) 775–791 (in Russian)

    MathSciNet  Google Scholar 

  17. V.Paulauskas "Non-uniform estimate in the central limit theorem in a separable Hilbert space", Proc.of the Third Japan-USSR Symp. on Probab.,Lecture Notes in Math. 550 (1976), 475–499.

    Google Scholar 

  18. V. Paulauskas, "The estimate of the rate of convergence in the central limit theorem in C(S)". Liet.matem.rink., 16, 4 (1976) 168–201 (in Russian)

    MathSciNet  MATH  Google Scholar 

  19. V. Paulauskas, letter to editors, Teor.verojat.i primen. 23, 2 (1978) p. 477 (in Russian)

    MathSciNet  Google Scholar 

  20. V.Paulauskas "Limit theorems for sums of independent random variables in Banach spaces", Doct.thesis, Vilnius, 1978 (in Russian)

    Google Scholar 

  21. V.Paulauskas "The rates of convergence to stable laws and the law of the iterated logarithm in Hilbert space, Univ. of Goteborg, Depart. of Math. Nr.5 (1977)

    Google Scholar 

  22. V.Paulauskas "The estimate of the rate of convergence in the central limit theorem in spaces Ip", submitted to Liet.matem.rink.

    Google Scholar 

  23. V.Paulauskas, A.Rackauskas "Infinitely divirsible and stable laws in separable Banach spaces II", to appear in Liet.matem.rink.

    Google Scholar 

  24. V.V. Sazonov, On ω2 criterion, Sankhya, ser. A, 30, 2 (1968) 205–210.

    MathSciNet  MATH  Google Scholar 

  25. V.V. Sazonov "An improvement of one estimate of rate of convergence" Teor.verojat.i primen. 14, 4 (1969) 667–678 (in Russian).

    MathSciNet  MATH  Google Scholar 

  26. N.N. Vakhanija, N.P. Kandelaki, "On estimate of the rate of convergence in the central limit theorem in Hilbert space" Transactions of Computer Center of AN. GSSR, 9, 1 (1969) 150–160.

    MathSciNet  Google Scholar 

  27. V.M. Zolotarev "Ideal metrics in the problem of approximation of distributions of sums of independent random variables", Teor.verojat.i primen. 22, 3 (1979) 449–465.

    MathSciNet  MATH  Google Scholar 

  28. V.M. Zolotarev, Metric distances in the spaces of random variables and their distributions, Matem.sbornik, 101 (143), 3, (1976) 104–141.

    MathSciNet  Google Scholar 

  29. V.M. Zolotarev, Approximation of the distribution of sums of independent random variables with values in infinite-dimensional spaces, Teor.verojat.i primen. 21, 4 (1976) 741–757.

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Vilnius V. Kapsukas University, 232042, Vilnius, Russia

    V. Paulauskas

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  1. V. Paulauskas
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A. Weron

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© 1980 Springer-Verlag

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Paulauskas, V. (1980). The rates of convergence in the central limit theorem in Banach spaces. In: Weron, A. (eds) Probability Theory on Vector Spaces II. Lecture Notes in Mathematics, vol 828. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097408

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  • DOI: https://doi.org/10.1007/BFb0097408

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10253-3

  • Online ISBN: 978-3-540-38350-5

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