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Upper estimate of martingale dimension for self-similar fractals
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  • Published: 13 July 2012

Upper estimate of martingale dimension for self-similar fractals

  • Masanori Hino1 

Probability Theory and Related Fields volume 156, pages 739–793 (2013)Cite this article

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Abstract

We study upper estimates of the martingale dimension d m of diffusion processes associated with strong local Dirichlet forms. By applying a general strategy to self-similar Dirichlet forms on self-similar fractals, we prove that d m  = 1 for natural diffusions on post-critically finite self-similar sets and that d m is dominated by the spectral dimension for the Brownian motion on Sierpinski carpets.

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Authors and Affiliations

  1. Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

    Masanori Hino

Authors
  1. Masanori Hino
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Corresponding author

Correspondence to Masanori Hino.

Additional information

Dedicated to Professor Leonard Gross on the occasion of his 80th birthday.

This research was partially supported by KAKENHI (21740094, 24540170).

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Cite this article

Hino, M. Upper estimate of martingale dimension for self-similar fractals. Probab. Theory Relat. Fields 156, 739–793 (2013). https://doi.org/10.1007/s00440-012-0442-3

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  • Received: 02 October 2011

  • Revised: 17 June 2012

  • Published: 13 July 2012

  • Issue Date: August 2013

  • DOI: https://doi.org/10.1007/s00440-012-0442-3

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Keywords

  • Martingale dimension
  • Self-similar set
  • Sierpinski carpet
  • Dirichlet form

Mathematics Subject Classification (2000)

  • 60G44
  • 28A80
  • 31C25
  • 60J60
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