Asymptotically one-dimensional diffusions on the Sierpinski gasket and the abc-gaskets

Kumiko Hattori, Tetsuya Hattori, Hiroshi Watanabe

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

Diffusion processes on the Sierpinski gasket and the abc-gaskets are constructed as limits of random walks. In terms of the associated renormalization group, the present method uses the inverse trajectories which converge to unstable fixed points corresponding to the random walks on one-dimensional chains. In particular, non-degenerate fixed points are unnecessary for the construction. A limit theorem related to the discrete-time multi-type non-stationary branching processes is applied.

Original languageEnglish
Pages (from-to)85-116
Number of pages32
JournalProbability Theory and Related Fields
Volume100
Issue number1
DOIs
Publication statusPublished - 1994 Mar
Externally publishedYes

Fingerprint

Sierpinski Gasket
Random walk
Fixed point
Multitype
Nonstationary Processes
Branching process
Limit Theorems
Renormalization Group
Diffusion Process
Discrete-time
Unstable
Trajectory
Converge
Nonstationary processes
Diffusion process
Limit theorems

Keywords

  • Mathematics Subject Classification: 60J60, 60J25, 60J85, 60J15

ASJC Scopus subject areas

  • Statistics and Probability
  • Analysis
  • Mathematics(all)

Cite this

Asymptotically one-dimensional diffusions on the Sierpinski gasket and the abc-gaskets. / Hattori, Kumiko; Hattori, Tetsuya; Watanabe, Hiroshi.

In: Probability Theory and Related Fields, Vol. 100, No. 1, 03.1994, p. 85-116.

Research output: Contribution to journalArticle

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