Transition densities for Brownian motion on the Sierpinski carpet
type: Item
instance of: scholarly article
title: Transition densities for Brownian motion on the Sierpinski carpet
zbMATH Open document ID: 0739.60071
DOI: 10.1007/BF01192060
publication date: 1992-06-28T00:00:00Z
review text: Upper and lower bounds are obtained for the transition densities \(p(t,x,y)\) of Brownian motion on the Sierpinski carpet. These are of the same form as those which hold for the Sierpinski gasket. In addition, the joint continuity of \(p(t,x,y)\) is proved, the existence of the spectral dimension is established, and the Einstein relation, connecting the spectral dimension, the Hausdorff dimension and the resistance exponent is shown to hold.
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 31361
zbMATH Keywords: Brownian motion on the Sierpinski carpet
zbMATH Keywords: spectral dimension
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: resistance exponent
author: Martin T. Barlow
author: Richard F. Bass
MaRDI profile type: Publication
cites work: Necessary and sufficient conditions for the continuity of local time of Lévy processes
cites work: The construction of Brownian motion on the Sierpinski carpet
cites work: Local times for Brownian motion on the Sierpinski carpet
cites work: On the resistance of the Sierpiński carpet
cites work: Resistance and spectral dimension of Sierpinski carpets
cites work: Brownian motion on the Sierpinski gasket
cites work: Some potential theory for reflecting Brownian motion in Hölder and Lipschitz domains
cites work: A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash
cites work: Q3855442
cites work: On the limiting distribution of a supercritical branching process in a random environment
cites work: Brownian motion on nested fractals
cites work: Sample path properties of the local times of strongly symmetric Markov processes via Gaussian processes
cites work: Isoperimetric constants and estimates of heat kernels of pre Sierpinski carpets
cites work: Spectral dimension of a wire network
cites work: Q3263029
full work available at URL: https://doi.org/10.1007/bf01192060
OpenAlex ID: W2072284288
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 31361