Uniqueness of Nelson's diffusions. II: Infinite dimensional setting and applications
type: Item
instance of: scholarly article
title: Uniqueness of Nelson's diffusions. II: Infinite dimensional setting and applications
zbMATH Open document ID: 0986.60074
DOI: 10.1023/A:1008707703191
published in: Potential Analysis
publication date: 2002-05-29T00:00:00Z
review text: [For part I see Probab. Theory Relat. Fields 114, No. 4, 549-585 (1999; Zbl 0936.60072).] It is proved that the generalized Schrödinger operator \({\mathcal L}^\varphi={\mathcal L}+ 2\Gamma(\varphi,\cdot)/\varphi\) generates a unique \(C_0\)-semigroup in \(L'\). Here \({\mathcal L}\) is the generator of a diffusion and \(\Gamma\) is the carré-du-champs operator of Meyer: \(2\Gamma(f,g)={\mathcal L}(fg)- f{\mathcal L}g- ({\mathcal L}f)g\), \(f,g\in {\mathcal D}({\mathcal L})\).
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 81Q10
zbMATH DE Number: 1569537
zbMATH Keywords: diffusion
zbMATH Keywords: Schrödinger operator
zbMATH Keywords: \(C_0\)-semigroup
author: Liming Wu
reviewed by: Murali Rao
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1569537