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• W2963380543 abstract "The derivative of self-intersection local time (DSLT) for Brownian motion was introduced by Rosen (Ros05) and subsequently used by others to study the L 2 andL 3 moduli of continuity of Brownian local time. A version of the DSLT for fractional Brownian motion (fBm) was introduced in (YYL08); however, the definition given there presents difficulties, since it is motivated by an inco rrect application of Ito's formula. To rectify this, we introduce a modified DSLT for fBm and prove existence using an explicit Wiener chaos expansion. We will then argue that our modification is the natural version of the DSLT by rigorously proving the corresponding Tanaka formula. This formula corrects a formal identity given in both (Ros05) and (YYL08). In the course of this endeavor we prove a Fubini theorem for integrals with respect to fBm. The Fubini theorem may be of independent interest, as it generalizes (to Hida distributions) similar results previously seen in the lite rature. As a further byproduct of our investigation, we also provide a correction to an important technical second- moment bound for fBm given in (Hu01)." @default.
• W2963380543 created "2019-07-30" @default.
• W2963380543 creator A5068977788 @default.
• W2963380543 creator A5086353857 @default.
• W2963380543 date "2014-01-01" @default.
• W2963380543 modified "2023-09-27" @default.
• W2963380543 title "On the Tanaka formula for the derivative of self-intersection local time of fractional Brownian motion" @default.
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• W2963380543 hasPublicationYear "2014" @default.
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