Simple method of obtaining estimates in the invariance principle

  • A. I. Sakhanenko
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1299)

Keywords

Joint Distribution Central Limit Theorem Invariance Principle Functional Central Limit Theorem Random Variable Versus 
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References

  1. [1]
    Feller W. An introduction to probability theory and its applications. V.2. New York: Wiley, 1971.MATHGoogle Scholar
  2. [2]
    Lévy P. Théorie de l'addition des variables aléatoires. Pairs: Gauthier-Villars, 1937.MATHGoogle Scholar
  3. [3]
    Bolthausen E. Exact convergence rates in some martingale central limit theorems. Ann. Probability, 1982, v.10, N3, 672–688.MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    Bentkus V., Raĉkauskas A. Estimates of distances between sums of independent random elements in Banach spaces. Teor. Verojatn. i Primenen., 1984, v.29, N1, 49–64 (in Russian).MATHGoogle Scholar
  5. [5]
    Bentkus V. Asymptotic analysis of sums of independent random elements of Banach space. Doctoral dissertation: Vilnius, 1985 (in Russian).Google Scholar
  6. [6]
    Borovkov A. A. On the rate of convergence for the invariance principle. Theory Probab. Appl., 1973, v.18, N2, 207–225.MathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    Berkes I., Philipp W. Approximation theorems for independent and weakly dependent random vectors. Ann. Probability, 1979, v.7, N1, 29–54.MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    Sakhanenko A. I. Estimates in invariance principle. Proc. Inst. Math. Novosibirsk, 1985, v.5, 37–44 (in Russian).MathSciNetMATHGoogle Scholar
  9. [9]
    Hall P., Heyde C. C. Martingale limit theory and its application. New York: Academic Press, 1980.MATHGoogle Scholar
  10. [10]
    Utev S. A. A remark on the rate of convergence in the invariance principle. Sibirsk. Mat. Z., 1981, v.22, N5, 206–208 (in Russian).MathSciNetMATHGoogle Scholar
  11. [11]
    Haeusler E. An exact rate of convergence in the functional central limit theorem for special martingale difference arrays. Z. Wahrscheinlichkeitstheorie verw. Gebiete, 1984, v.65, N4, 523–534.MathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    Borovkov K. A. On the invariance principle in Hilbert space. Teor. Verojatn. i Primenen., 1983, v.28, N3, 603 (in Russian).Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • A. I. Sakhanenko
    • 1
  1. 1.Institute of MathematicsNovosibirskUSSR

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