Generalized positive continuous additive functionals of multidimensional Brownian motion and their associated Revuz measures

H. Uemura

Stochastic Processes and their Applications, 2008, vol. 118, issue 10, 1870-1891

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.

Keywords: Positive; continuous; additive; functional; Local; time; Revuz; measure; Ito-Wiener; chaos; expansion (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (1)

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