RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Zametki, 1978, Volume 23, Issue 3, Pages 447–462 (Mi mz8160)  

Entropy of stochastic processes homogeneous with respect to a commutative group of transformations

B. S. Pitskel'

Moscow Institute of Railroad Engineering,

Abstract: In order to define the entropy of a stochastic field homogeneous with respect to a countable commutative group of transformations $G$, one fixes a sequence $\{A_n\}$ of finite subsets of the group $G$ and considers the upper limit of the sequence of mean entropies of the iterates of the decomposition $P$. i.e., $\varlimsup\limits_{n\to\infty}|A_n|^{-1}H\cdot(\bigvee\limits_{g\in R}T_gP)$, where $|A_n|$ is the number of elements in $A_n$. It is proved that for a fixed stochastic field and all sequences $\{A_n\}$ satisfying the Folner condition, the limit of the means exists and is unique. If the sequence $\{A_n\}$ is such that for all stochastic fields invariant under $G$, the entropy calculated in terms of it is the same as that calculated for a Folner-sequence, then $\{A_n\}$ satisfies the Folner condition. In the case when $G$ is a $\bar\nu$-dimensional lattice $Z^\nu$, the Folner condidition coincides with the Van Hove condition.

Full text: PDF file (1073 kB)

English version:
Mathematical Notes, 1978, 23:3, 242–250

Bibliographic databases:

UDC: 513.6
Received: 18.12.1975

Citation: B. S. Pitskel', “Entropy of stochastic processes homogeneous with respect to a commutative group of transformations”, Mat. Zametki, 23:3 (1978), 447–462; Math. Notes, 23:3 (1978), 242–250

Citation in format AMSBIB
\Bibitem{Pit78}
\by B.~S.~Pitskel'
\paper Entropy of stochastic processes homogeneous with respect to a~commutative group of transformations
\jour Mat. Zametki
\yr 1978
\vol 23
\issue 3
\pages 447--462
\mathnet{http://mi.mathnet.ru/mz8160}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=494449}
\zmath{https://zbmath.org/?q=an:0405.60013|0394.60011}
\transl
\jour Math. Notes
\yr 1978
\vol 23
\issue 3
\pages 242--250
\crossref{https://doi.org/10.1007/BF01651440}


Linking options:
  • http://mi.mathnet.ru/eng/mz8160
  • http://mi.mathnet.ru/eng/mz/v23/i3/p447

    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
  • Математические заметки Mathematical Notes
    Number of views:
    This page:108
    Full text:52
    First page:1

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