Ukrainian Mathematical Journal

, Volume 52, Issue 2, pp 305–318 | Cite as

On the rosenthal inequality for mixing fields

  • I. Fazekas
  • A. G. Kukush
  • T. Tómács


A proof of the Rosenthal inequality for α-mixing random fields is given. The statements and proofs are modifications of the corresponding results obtained by Doukhan and Utev.


Connected Graph Independent Random Variable Finite Subset Separable Banach Space Dependent Random Variable 
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  1. 1.
    I. Fazekas and A. G. Kukush, “Asymptotic properties of an estimator in nonlinear functional errors-in-variables models with dependent error terms”, Comput. Math. Appl., 34, No. 10, 23–39 (1997).zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    H. P. Rosenthal, “On the subspaces of L p (p > 2) spanned by sequences of independent random variables”, Isr. J. Math., 8, 273–303 (1970).zbMATHCrossRefGoogle Scholar
  3. 3.
    S. A. Utev, “Inequalities for sums of weakly dependent random variables and rate of convergence in invariance principle,” in: Limit Theorems for Sums of Random Variables [in Russian], Nauka, Novosibirsk (1984), pp. 50–70.Google Scholar
  4. 4.
    P. Doukhan, Mixing. Properties and Example, Springer, New York 1994.Google Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 2000

Authors and Affiliations

  • I. Fazekas
    • 1
  • A. G. Kukush
    • 2
  • T. Tómács
    • 3
  1. 1.Kossuth UniversityDebrecenHungary
  2. 2.Kiev UniversityKiev
  3. 3.Teacher’s Training CollegeEgerHungary

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