Mathematical Notes

, Volume 78, Issue 1–2, pp 47–52 | Cite as

Estimates of the Entropy of the Set of Means for Some Classes of Stationary and Quasistationary Sequences

  • V. F. Gaposhkin


We consider the set of arithmetic means for some classes of stationary and quasistationary sequences. Order-sharp estimates of the entropy of this set for the classes under consideration are given.

Key words

set of arithmetic means entropy of the set of arithmetic means stationary sequence quasistationary sequence spectral measure 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Talagrand, “Applying a theorem of Fernique,” Ann. Inst. H. Poincare, 32 (1996), 779–799.Google Scholar
  2. 2.
    M. Weber, Entropie metrique et convergence presque partout, Hermann, Paris, 1998.Google Scholar
  3. 3.
    C. Gamet and M. Weber, “Entropy numbers of some ergodic averages,” Teor. Veroyatnost. i Primenen. [Theory Probab. Appl.], 44 (1999), no. 4, 776–795.Google Scholar
  4. 4.
    V. F. Gaposhkin, “Convergence of series related to stationary sequences” Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.], 39 (1975), no. 6, 1365–1392.Google Scholar
  5. 5.
    V. F. Gaposhkin, “Decrease rate of the probabilities of ε-deviations for the means of stationary processes,” Mat. Zametki [Math. Notes], 64 (1998), no. 3, 366–372.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • V. F. Gaposhkin
    • 1
  1. 1.Moscow State University of Railway EngineeringMoscowRussia

Personalised recommendations