Uniqueness of Nelson's diffusions
type: Item
instance of: scholarly article
title: Uniqueness of Nelson's diffusions
zbMATH Open document ID: 0936.60072
publication date: 2000-05-09T00:00:00Z
review text: The paper is a continuation of the previous work [J. Funct. Anal. 153, No. 2, 276-319 (1998; Zbl 0913.35035)] on uniqueness of Schrödinger operators restricted to the domain. The present paper addresses the problem whether a generator of the Nelson diffusion, defined on \(C^\infty_0 (D)\) where \(D\subset R^d\) is an open domain, generates a unique semigroup in \(L^1 (D,\varphi^2 dx)\). The central result of the paper is Theorem 2.1 which sets a sufficient and necessary condition for the Nelson generator to be closable. That implies that its extension generates a unique semigroup of class \(C_0\) on \(L^1\). The nonuniqueness of the semigroup in \(L^2(D, \varphi^2dx)\), in the presence of nodal sets (unattainable barriers), is established in Section 4.
reviewed by: Piotr Garbaczewski
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 81Q10
zbMATH DE Number: 1339334
zbMATH Keywords: strong Feller property
zbMATH Keywords: Dirichlet forms
zbMATH Keywords: Nelson diffusions
zbMATH Keywords: semigroups
zbMATH Keywords: node sets
author: Liming Wu
MaRDI profile type: Publication
full work available at URL: s004400050234
OpenAlex ID: W2318238767
DOI: 10.1007/S004400050234
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 1339334