From one dimensional diffusions to symmetric Markov processes
type: Item
instance of: scholarly article
title: From one dimensional diffusions to symmetric Markov processes
zbMATH Open document ID: 1221.60113
author: Masatoshi Fukushima
published in: Stochastic Processes and their Applications
publication date: 2010-05-21T00:00:00Z
review text: Let \(X^0\) be an absorbing diffusion on a one-dimensional regular interval \(I\), with scale function \(s\), speed measure \(m\), and no killing inside. The first aim of the paper is to identify the Dirichlet form of \(X^0\) on \(L^2(I,m)\) and its extended Dirichlet space in terms of the scale function \(s\). Once the Dirichlet form has been identified, one can consider all possible symmetric extension of \(X^0\). The maximal extension corresponds to the concept of the reflected Dirichlet space. The author also discusses the possibility of symmetric extensions of a time changed transient reflecting Brownian motion on a closed domain in \(\mathbb R^d\), \(d\geq 3\), possessing two branches of infinite cones.
reviewed by: Zoran Vondraček
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J50
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 31C25
zbMATH DE Number: 5710796
zbMATH Keywords: diffusion
zbMATH Keywords: time change
zbMATH Keywords: Dirichlet form
zbMATH Keywords: reflecting extension
MaRDI profile type: Publication
full work available at URL: j.spa.2010.01.010
OpenAlex ID: W1966107808
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DOI: 10.1016/J.SPA.2010.01.010
description: scientific article; zbMATH DE number 5710796