The gauge theorem for a class of additive functionals of zero energy

Joseph Glover, Murali Rao, Renming Song

Research output: Contribution to journalArticlepeer-review


In earlier works, the gauge theorem was proved for additive functionals of Brownian motion of the form ∫0tq(Bs)ds, where q is a function in the Kato class. Subsequently, the theorem was extended to additive functionals with Revuz measures μ 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.

Original languageEnglish (US)
Pages (from-to)195-210
Number of pages16
JournalProbability Theory and Related Fields
Issue number1-2
StatePublished - Mar 1993
Externally publishedYes


  • Mathematics Subject Classification (1991): 60J65, 60J55, 60J57

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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