The gauge theorem for a class of additive functionals of zero energy
نویسندگان
چکیده
In earlier works, the gauge theorem was proved for additive functionals of Brownian motion of the form f ~o q(Bs)ds, where q is a function in the Kato class. Subsequently, the theorem was extended to additive functionals with Revuz measures/ t 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.
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