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

Kumiko Hattori; Tetsuya Hattori; Hiroshi Watanabe

doi:10.1007/BF01204955

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

Kumiko Hattori, Tetsuya Hattori, Hiroshi Watanabe

Research output: Contribution to journal › Article › peer-review

17 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 language	English
Pages (from-to)	85-116
Number of pages	32
Journal	Probability Theory and Related Fields
Volume	100
Issue number	1
DOIs	https://doi.org/10.1007/BF01204955
Publication status	Published - 1994 Mar
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/BF01204955

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AB - 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.

KW - Mathematics Subject Classification: 60J60, 60J25, 60J85, 60J15

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

Abstract

Keywords

ASJC Scopus subject areas

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