کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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1156387 | 958826 | 2008 | 22 صفحه PDF | دانلود رایگان |
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.
Journal: Stochastic Processes and their Applications - Volume 118, Issue 10, October 2008, Pages 1870–1891