Brownian motion on the continuum tree
type: Item
instance of: scholarly article
title: Brownian motion on the continuum tree
zbMATH Open document ID: 0822.60069
DOI: 10.1007/BF01200505
publication date: 1995-10-05T00:00:00Z
review text: The author constructs a so-called Brownian motion on the continuum tree, that is a continuous symmetric Markov process with further special properties of hitting times of points. The elegant construction relies on the theory of Dirichlet forms. Typically, a continuous Markov process \(X^ 0\) is first obtained as the diffusion associated to some regular local Dirichlet form; and then the Brownian motion \(X\) is defined by a time-change of \(X^ 0\) based on an adequate additive functional. Moreover, one can establish the existence of a jointly continuous version of the local times of \(X^ 0\), using recent results of \textit{M. B. Marcus} and \textit{J. Rosen} [Ann. Probab. 20, No. 4, 1603-1684 (1992; Zbl 0762.60068)].
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 60J55
zbMATH DE Number: 751358
zbMATH Keywords: Brownian motion
zbMATH Keywords: continuum tree
zbMATH Keywords: Dirichlet form
zbMATH Keywords: local times
author: William B. Krebs
reviewed by: Jean Bertoin
MaRDI profile type: Publication
cites work: Classical Dirichlet forms on topological vector spaces --- closability and a Cameron-Martin formula
cites work: The continuum random tree. I
cites work: The continuum random tree. III
cites work: The construction of Brownian motion on the Sierpinski carpet
cites work: Local times for Brownian motion on the Sierpinski carpet
cites work: Transition densities for Brownian motion on the Sierpinski carpet
cites work: Brownian motion on the Sierpinski gasket
cites work: Q3855442
cites work: Brownian motion on a homogeneous fractal
cites work: Brownian motion on nested fractals
cites work: Random Fourier Series with Applications to Harmonic Analysis. (AM-101)
cites work: Sample path properties of the local times of strongly symmetric Markov processes via Gaussian processes
cites work: Q4040434
cites work: Dirichlet spaces and random time change
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 751358