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Siberian Mathematical Journal

, Volume 26, Issue 1, pp 7–15 | Cite as

Exponential estimates for distributions of sums of independent random fields

  • I. S. Borisov
Article

Keywords

Random Field Exponential Estimate Independent Random Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature Cited

  1. 1.
    R. M. Dudley and W. Philipp, “Invariance principles for sums of Banach space valued random elements and empirical processes,” Z. Wahrscheinlichkeitstheorie Verw. Geb.,62, No. 4, 509–552 (1983).Google Scholar
  2. 2.
    R. M. Dudley, “Empirical and Poisson processes on classes of sets or functions too large for the central limit theorem,” Z. Wahrscheinlichkeitstheorie Verw. Geb.,61, No. 3, 355–368 (1982).Google Scholar
  3. 3.
    J. Kuelbs and R. M. Dudley, “Log log laws for empirical measures,” Ann. Proab.,8, No. 3, 405–418 (1980).Google Scholar
  4. 4.
    I. S. Borisov, “The problem of exactness of approximation in the central limit theorem for empirical measures,” Sib. Mat. Zh.,24, No. 6, 14–25 (1983).Google Scholar
  5. 5.
    V. V. Yurinskii, “Exponential inequalities for sums of random vectors,” J. Multivar. Anal.,6, No. 4, 473–499 (1976).Google Scholar
  6. 6.
    I. S. Borisov, “The speed of convergence in the central limit theorem for empirical measures,” Tr. Inst. Mat. Sib. Otd. Akad. Nauk SSSR,3, 125–143 (1984).Google Scholar
  7. 7.
    P. Gänssler, “On the Glivenko-Cantelli theorem,” Colloquia Math. Societatis Janos Bolyai,11, 93–103 (1974).Google Scholar
  8. 8.
    K. Krickeberg, “An alternative approach to the Glivenko-Cantelli theorem” Lect. Notes Math.,566, 57–67 (1976).Google Scholar
  9. 9.
    J. Dehardt, “Generalizations of the Glivenko-Centelli theorem,” Ann. Math. Statist.,42, No. 6, 2050–2055 (1971).Google Scholar
  10. 10.
    V. V. Petrov, Sums of Independent Random Variables, Springer-Verlag (1975).Google Scholar
  11. 11.
    M. Durst and R. M. Dudley, “Empirical processes, Vapnik-Chervonenkis classes and Poisson processes,” Probab. Math. Stat.,1, No. 2, 109–115 (1981).Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • I. S. Borisov

There are no affiliations available

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