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A Clark-Ocone formula in UMD Banach space | | Jan Maas
; Jan van Neerven
; | | Date: |
13 Sep 2007 | | Abstract: | Let H be a separable real Hilbert space and let F = (F_t)_{tin [0,T]} be the
augmented filtration generated by an H-cylindrical Brownian motion W_H on
[0,T]. We prove that if E is a UMD Banach space, 1leq p<infty, and fin
D^{1,p}(E) is F_T-measurable, then f = E f + int_0^T P_F(Df) dW_H where D is
the Malliavin derivative and P_F is the projection onto the F-adapted elements
in a suitable Banach space of L^p-stochastically integrable L(H,E)-valued
processes. | | Source: | arXiv, 0709.2021 | | Services: | Forum | Review | PDF | Favorites | |
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