A Clark-Ocone formula in UMD Banach spaces
Probability
2008-03-04 v2 Functional Analysis
Abstract
Let H be a separable real Hilbert space and let F = (F_t)_{t\in [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, 1\leq p<\infty, and f\in 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.
Keywords
Cite
@article{arxiv.0709.2021,
title = {A Clark-Ocone formula in UMD Banach spaces},
author = {Jan Maas and Jan van Neerven},
journal= {arXiv preprint arXiv:0709.2021},
year = {2008}
}
Comments
12 pages; revised version, to appear in Electronic Communications in Probability