Homogenization of nested fractals
type: Item
instance of: scholarly article
title: Homogenization of nested fractals
zbMATH Open document ID: 0843.31004
DOI: 10.1007/BF01213686
author: Takashi Kumagai
author: Shigeo Kusuoka
publication date: 1996-05-13T00:00:00Z
review text: We study the homogenization problem on nested fractals. Let \(X_t\) be the continuous time Markov chain on the pre-nested fractal given by putting i.i.d. random resistors on each cell. It is proved that under some conditions, \(\alpha^{-n} X_{t^n_E t}\) converges in law to a constant time change of the Brownian motion on the fractal as \(n\to \infty\), where \(\alpha\) is the contraction rate and \(t_E\) is a time scale constant. As the Brownian motion on fractals is not a semi-martingale, we need a different approach from the well-developed martingale method.
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 47A35
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 878011
zbMATH Keywords: homogenization problem on nested fractals
zbMATH Keywords: Markov chain
zbMATH Keywords: Brownian motion on fractals
zbMATH Keywords: martingale method
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 878011