The gauge theorem for a class of additive functionals of zero energy
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.
scientific article; zbMATH DE number 568987
scientific article