The gauge theorem for a class of additive functionals of zero energy
type: Item
instance of: scholarly article
title: The gauge theorem for a class of additive functionals of zero energy
zbMATH Open document ID: 0792.60070
DOI: 10.1007/BF01199320
author: Joseph Glover
author: Murali Rao
author: Renming Song
publication date: 1994-07-24T00:00:00Z
review text: In earlier works, the gauge theorem was proved for additive functionals of Brownian motion of the form \(\int^ t_ 0 q(B_ s)ds\), where \(q\) is a function in the Kato class. Subsequently, the theorem was extended to additive functionals with Revuz measures \(\mu\) in the Kato class. We prove that the gauge theorem holds for a large class of additive functionals of zero energy which are, in general, of unbounded variation. These additive functionals may not be semi-martingales, but correspond to a collection of distributions that belong to the Kato class in a suitable sense. Our gauge theorem generalizes the earlier versions of the gauge theorem.
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60J57
zbMATH DE Number: 568987
zbMATH Keywords: additive functionals of Brownian motion
zbMATH Keywords: additive functionals
zbMATH Keywords: semi- martingales
zbMATH Keywords: gauge theorem
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 568987