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Simple method of obtaining estimates in the invariance principle

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Book cover Probability Theory and Mathematical Statistics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1299))

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References

  1. Feller W. An introduction to probability theory and its applications. V.2. New York: Wiley, 1971.

    MATH  Google Scholar 

  2. Lévy P. Théorie de l'addition des variables aléatoires. Pairs: Gauthier-Villars, 1937.

    MATH  Google Scholar 

  3. Bolthausen E. Exact convergence rates in some martingale central limit theorems. Ann. Probability, 1982, v.10, N3, 672–688.

    Article  MathSciNet  MATH  Google Scholar 

  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).

    MATH  Google Scholar 

  5. Bentkus V. Asymptotic analysis of sums of independent random elements of Banach space. Doctoral dissertation: Vilnius, 1985 (in Russian).

    Google Scholar 

  6. Borovkov A. A. On the rate of convergence for the invariance principle. Theory Probab. Appl., 1973, v.18, N2, 207–225.

    Article  MathSciNet  MATH  Google Scholar 

  7. Berkes I., Philipp W. Approximation theorems for independent and weakly dependent random vectors. Ann. Probability, 1979, v.7, N1, 29–54.

    Article  MathSciNet  MATH  Google Scholar 

  8. Sakhanenko A. I. Estimates in invariance principle. Proc. Inst. Math. Novosibirsk, 1985, v.5, 37–44 (in Russian).

    MathSciNet  MATH  Google Scholar 

  9. Hall P., Heyde C. C. Martingale limit theory and its application. New York: Academic Press, 1980.

    MATH  Google Scholar 

  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).

    MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  12. Borovkov K. A. On the invariance principle in Hilbert space. Teor. Verojatn. i Primenen., 1983, v.28, N3, 603 (in Russian).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, 630090, Novosibirsk, USSR

    A. I. Sakhanenko

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  1. A. I. Sakhanenko
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Shinzo Watanabe Jurii Vasilievich Prokhorov

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© 1988 Springer-Verlag

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Sakhanenko, A.I. (1988). Simple method of obtaining estimates in the invariance principle. In: Watanabe, S., Prokhorov, J.V. (eds) Probability Theory and Mathematical Statistics. Lecture Notes in Mathematics, vol 1299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078502

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  • DOI: https://doi.org/10.1007/BFb0078502

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18814-8

  • Online ISBN: 978-3-540-48187-4

  • eBook Packages: Springer Book Archive

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