Generalized positive continuous additive functionals of multidimensional Brownian motion and their associated Revuz measures |
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Authors: | H. Uemura |
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Affiliation: | Department of Mathematics Education, Aichi University of Education, Kariya, Aichi 448-8542, Japan |
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Abstract: | We extend the notion of positive continuous additive functionals of multidimensional Brownian motions to generalized Wiener functionals in the setting of Malliavin calculus. We call such a functional a generalized PCAF. The associated Revuz measure and a characteristic of a generalized PCAF are also extended adequately. By making use of these tools a local time representation of generalized PCAFs is discussed. It is known that a Radon measure corresponds to a generalized Wiener functional through the occupation time formula. We also study a condition for this functional to be a generalized PCAF and the relation between the associated Revuz measure of the generalized PCAF corresponding to Radon measure and this Radon measure. Finally we discuss a criterion to determine the exact Meyer–Watanabe’s Sobolev space to which this corresponding functional belongs. |
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Keywords: | Positive continuous additive functional Local time Revuz measure Itô &ndash Wiener chaos expansion |
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