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Homogeneous diffusions on the Sierpinski gasket

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Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 1686)

Abstract

We prove that certain diffusions on the Sierpinski gasket may be characterized, up to a multiplicative constant in the time scale, by a parameter α∈[0, 1/4]. The diffusions considered have the Feller property and certain natural symmetry properties, but they are not necessarily scale invariant. The case α=0 corresponds roughly speaking to one-dimensional Brownian motion and the case α=1/4 corresponds to Brownian motion on the Sierpinski gasket.

Keywords

  • Brownian Motion
  • Random Walk
  • Multiplicative Constant
  • Sierpinski Gasket
  • Theory Relate Field

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© 1998 Springer-Verlag

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Heck, M.K. (1998). Homogeneous diffusions on the Sierpinski gasket. In: Azéma, J., Yor, M., Émery, M., Ledoux, M. (eds) Séminaire de Probabilités XXXII. Lecture Notes in Mathematics, vol 1686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101753

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  • DOI: https://doi.org/10.1007/BFb0101753

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64376-0

  • Online ISBN: 978-3-540-69762-6

  • eBook Packages: Springer Book Archive