The gauge theorem for a class of additive functionals of zero energy |
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Authors: | Joseph Glover Murali Rao Renming Song |
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Institution: | (1) Department of Mathematics, University of Florida, 32611 Gainesville, FL, USA |
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Abstract: | Summary In earlier works, the gauge theorem was proved for additive functionals of Brownian motion of the form
0
t
q(B
s
)ds, whereq is a function in the Kato class. Subsequently, the theorem was extended to additive functionals with Revuz measures 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.Research supported in part by NSA grant MDA-92-H-30324 |
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Keywords: | 60J65 60J55 60J57 |
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