RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Guidelines for authors

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Probl. Peredachi Inf.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Probl. Peredachi Inf., 2001, Volume 37, Issue 2, Pages 27–39 (Mi ppi515)  

This article is cited in 2 scientific papers (total in 2 papers)

Large Systems

Nonrobustness Property of the Individual Ergodic Theorem

V. V. V'yugin


Abstract: Main laws of probability theory, when applied to individual sequences, have a “robustness” property under small violations of randomness. For example, the law of large numbers for the symmetric Bernoulli scheme holds for a sequence where the randomness deficiency of its initial fragment of length $n$ grows as $o(n)$. The law of iterated logarithm holds if the randomness deficiency grows as $o(\log\log n)$. We prove that Birkhoff's individual ergodic theorem is nonrobust in this sense. If the randomness deficiency grows arbitrarily slowly on initial fragments of an infinite sequence, this theorem can be violated. An analogous nonrobustness property holds for the Shannon–McMillan–Breiman theorem.

Full text: PDF file (1647 kB)
References: PDF file   HTML file

English version:
Problems of Information Transmission, 2001, 37:2, 108–119

Bibliographic databases:

UDC: 621.391.1:519.2
Received: 26.10.2000

Citation: V. V. V'yugin, “Nonrobustness Property of the Individual Ergodic Theorem”, Probl. Peredachi Inf., 37:2 (2001), 27–39; Problems Inform. Transmission, 37:2 (2001), 108–119

Citation in format AMSBIB
\Bibitem{Vyu01}
\by V.~V.~V'yugin
\paper Nonrobustness Property of the Individual Ergodic Theorem
\jour Probl. Peredachi Inf.
\yr 2001
\vol 37
\issue 2
\pages 27--39
\mathnet{http://mi.mathnet.ru/ppi515}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2099896}
\zmath{https://zbmath.org/?q=an:1012.37003}
\transl
\jour Problems Inform. Transmission
\yr 2001
\vol 37
\issue 2
\pages 108--119
\crossref{https://doi.org/10.1023/A:1010418008049}


Linking options:
  • http://mi.mathnet.ru/eng/ppi515
  • http://mi.mathnet.ru/eng/ppi/v37/i2/p27

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. V'yugin, “Problems of Robustness for Universal Coding Schemes”, Problems Inform. Transmission, 39:1 (2003), 32–46  mathnet  crossref  mathscinet  zmath
    2. V'yugin V.V., “on the Stability Property of Asymptotic Laws of Ergodic Theory and Universal Compression Schemes”, Dokl. Math., 92:2 (2015), 556–558  crossref  zmath  isi
  • Проблемы передачи информации Problems of Information Transmission
    Number of views:
    This page:279
    Full text:80
    References:27

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020