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Zap. Nauchn. Sem. POMI, 2005, Volume 325, Pages 103–112 (Mi znsl352)  

This article is cited in 1 scientific paper (total in 1 paper)

The $\sigma$-algebra of pasts of a random walk on the orbits of the Bernoulli action of the group $Z^d$

A. D. Gorbul'skii

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: In the present paper, we study the $\sigma$-algebra of pasts $\Xi=\{\xi_n\}_n$ of a random walk $\mathcal T$ on the orbits of the Bernoulli action of the group $Z^d$. The proper scaling and the scaling entropy of this sequence of partitions is calculated. We show that the proper scaling entropy of the $\sigma$-algebra of pasts is $h(\Xi)=\frac1{2d}\log(2d)$.

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English version:
Journal of Mathematical Sciences (New York), 2006, 138:3, 5686–5690

Bibliographic databases:

UDC: 519.218.82, 519.212.2
Received: 02.08.2005

Citation: A. D. Gorbul'skii, “The $\sigma$-algebra of pasts of a random walk on the orbits of the Bernoulli action of the group $Z^d$”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XII, Zap. Nauchn. Sem. POMI, 325, POMI, St. Petersburg, 2005, 103–112; J. Math. Sci. (N. Y.), 138:3 (2006), 5686–5690

Citation in format AMSBIB
\Bibitem{Gor05}
\by A.~D.~Gorbul'skii
\paper The $\sigma$-algebra of pasts of a~random walk on the orbits of the Bernoulli action of the group~$Z^d$
\inbook Representation theory, dynamical systems, combinatorial and algoritmic methods. Part~XII
\serial Zap. Nauchn. Sem. POMI
\yr 2005
\vol 325
\pages 103--112
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl352}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2160321}
\zmath{https://zbmath.org/?q=an:1084.37006}
\elib{http://elibrary.ru/item.asp?id=9126995}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2006
\vol 138
\issue 3
\pages 5686--5690
\crossref{https://doi.org/10.1007/s10958-006-0336-y}
\elib{http://elibrary.ru/item.asp?id=13532445}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748635620}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. M. Vershik, A. D. Gorbul'skii, “Scaled entropy of filtrations of $\sigma$-fields”, Theory Probab. Appl., 52:3 (2008), 493–508  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Записки научных семинаров ПОМИ
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