Teoriya Veroyatnostei i ee Primeneniya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Teor. Veroyatnost. i Primenen.:
Year:
Volume:
Issue:
Page:
Find






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


Teoriya Veroyatnostei i ee Primeneniya, 1999, Volume 44, Issue 3, Pages 589–616
DOI: https://doi.org/10.4213/tvp805
(Mi tvp805)
 

This article is cited in 10 scientific papers (total in 10 papers)

Dimension of random fractals in metric spaces

A. A. Tempel'manab

a Department of Mathematics, Pennsylvania State University, USA
b Department of Statistics, Pennsylvania State University, USA
Abstract: We study the local and Hausdorff dimensions of measures in function and sequence spaces and the Hausdorff dimension of such spaces with respect to deterministic and random ‘`scale metrics.’ Following ideas due to Billingsley and Furstenberg we show that the local dimension of a properly chosen probability measure is an efficient tool for the calculation of the Hausdorff dimension. In particular, the calculation of the Hausdorff dimension of a sequence space with respect to a deterministic scale metric with finite memory is reduced to the calculation of the local dimension of the associated Markov chain that can be found easily; both dimensions coincide with the solution of the generalized Moran equation specified by the scale metric. When the scale metric is random we come to a stochastic analogue of the Moran equation. These results are used as a ‘`leading special case’ in the study of the Hausdorff dimension of deterministic and random fractals in general metric spaces.
Keywords: Hausdorff dimension, Hausdorff measure, local dimension, Markov chain, fractal.
Received: 30.05.1997
Revised: 14.02.1998
English version:
Theory of Probability and its Applications, 2000, Volume 44, Issue 3, Pages 537–557
DOI: https://doi.org/10.1137/S0040585X97977756
Bibliographic databases:
Language: Russian
Citation: A. A. Tempel'man, “Dimension of random fractals in metric spaces”, Teor. Veroyatnost. i Primenen., 44:3 (1999), 589–616; Theory Probab. Appl., 44:3 (2000), 537–557
Citation in format AMSBIB
\Bibitem{Tem99}
\by A.~A.~Tempel'man
\paper Dimension of random fractals in metric spaces
\jour Teor. Veroyatnost. i Primenen.
\yr 1999
\vol 44
\issue 3
\pages 589--616
\mathnet{http://mi.mathnet.ru/tvp805}
\crossref{https://doi.org/10.4213/tvp805}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1805822}
\zmath{https://zbmath.org/?q=an:0972.28002}
\transl
\jour Theory Probab. Appl.
\yr 2000
\vol 44
\issue 3
\pages 537--557
\crossref{https://doi.org/10.1137/S0040585X97977756}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000090154300007}
Linking options:
  • https://www.mathnet.ru/eng/tvp805
  • https://doi.org/10.4213/tvp805
  • https://www.mathnet.ru/eng/tvp/v44/i3/p589
  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024