Dirichlet forms and Brownian motion penetrating fractals
type: Item
instance of: scholarly article
title: Dirichlet forms and Brownian motion penetrating fractals
zbMATH Open document ID: 0973.31009
DOI: 10.1023/A:1008601800611
author: Alf Jonsson
published in: Potential Analysis
publication date: 2001-11-15T00:00:00Z
review text: In 1993, \textit{T. Lindstrøm} [Pitman Res. Notes Math. Ser. 283, 148-278 (1993; Zbl 0787.60101)] proved that Brownian motion can penetrate the two-dimensional Sierpinski gasket in the sense that there exists a process which coincides with the ordinary Brownian motion outside the convex hull of the gasket and with the fractal Brownian motion in the gasket. In this paper, the author gives a different proof of this using the theory of Dirichlet forms. The proof of this paper also works in higher dimensions.
reviewed by: Renming Song
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 1523586
zbMATH Keywords: Dirichlet forms
zbMATH Keywords: Brownian motion
zbMATH Keywords: Sierpinski gasket
MaRDI profile type: Publication
full work available at URL: a:1008601800611
OpenAlex ID: W1586938224
description: scientific article; zbMATH DE number 1523586