A family of diffusion processes on Sierpinski carpets

研究成果: Contribution to journalArticle査読

5 被引用数 (Scopus)

抄録

We construct a family of diffusions Pα = {Px.} on the d-dimensional Sierpinski carpet F̂. The parameter α ranges over dH < α < ∞, where dH = log(3d - 1)/log 3 is the Hausdorff dimension of the d-dimensional Sierpinski carpet F̂. These diffusions Pα are reversible with invariant measures μ = μ[α]. Here, μ are Radon measures whose topological supports are equal to F̂ and satisfy self-similarity in the sense that μ(3A) = 3α · μ(A) for all A ∈ ℬ(F̂). In addition, the diffusion is self-similar and invariant under local weak translations (cell translations) of the Sierpinski carpet. The transition density p = p(t, x, y) is locally uniformly positive and satisfies a global Gaussian upper bound. In spite of these well-behaved properties, the diffusions are different from Barlow-Bass' Brownian motions on the Sierpinski carpet.

本文言語英語
ページ(範囲)275-310
ページ数36
ジャーナルProbability Theory and Related Fields
119
2
DOI
出版ステータス出版済み - 2 2001
外部発表はい

All Science Journal Classification (ASJC) codes

  • 分析
  • 統計学および確率
  • 統計学、確率および不確実性

フィンガープリント

「A family of diffusion processes on Sierpinski carpets」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル