Transition density estimates for Brownian motion on affine nested fractals

Pat J. Fitzsimmons*, Ben M. Hambly, Takashi Kumagai

*この研究の対応する著者

研究成果: Article査読

72 被引用数 (Scopus)

抄録

A class of affine nested fractals is introduced which have different scale factors for different similitudes but still have the symmetry assumptions of nested fractals. For these fractals estimates on the transition density for the Brownian motion are obtained using the associated Dirichlet form. An upper bound for the diagonal can be found using a Nash-type inequality, then probabilistic techniques are used to obtain the off-diagonal bound. The approach differs from previous treatments as it uses only the Dirichlet form and no estimates on the resolvent. The bounds obtained are expressed in terms of an intrinsic metric on the fractal.

本文言語English
ページ(範囲)595-620
ページ数26
ジャーナルCommunications in Mathematical Physics
165
3
DOI
出版ステータスPublished - 1994 10月
外部発表はい

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学

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