Estimates of transition densities for Brownian motion of nested fractals
type: Item
instance of: scholarly article
title: Estimates of transition densities for Brownian motion of nested fractals
zbMATH Open document ID: 0792.60073
DOI: 10.1007/BF01192133
author: Takashi Kumagai
publication date: 1994-07-24T00:00:00Z
review text: We obtain upper and lower bounds for the transition densities of Brownian motion on nested fractals. Compared with the estimate on the Sierpinski gasket, the results require the introduction of a new exponent, \(d_ J\), related to the ``shortest path metric'' and ``chemical exponent'' on nested fractals. Further, Hölder order of the resolvent densities, sample paths and local times are obtained. The results are obtained by using the theory of multi-type branching processes.
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 569088
zbMATH Keywords: nonstandard analysis
zbMATH Keywords: Dirichlet forms
zbMATH Keywords: transition densities of Brownian motion on nested fractals
zbMATH Keywords: multi-type branching processes
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 569088