article
A Clark-Ocone formula in UMD Banach spaces
published
Jan
Van Neerven
author
Jan
Maas
author 4C5696CE-F248-11E8-B48F-1D18A9856A870000-0002-0845-1338
Let H be a separable real Hubert space and let double struck F sign = (ℱt)t∈[0,T] be the augmented filtration generated by an H-cylindrical Brownian motion (WH(t))t∈[0,T] on a probability space (Ω, ℱ ℙ). We prove that if E is a UMD Banach space, 1 ≤ p < ∞, and F ∈ double struck D sign1,p(Ω E) is ℱT-measurable, then F = double struck E sign(F) + ∫0T Pdouble struck F sign(DF) dW H, where D is the Malliavin derivative of F and P double struck F sign is the projection onto the F-adapted elements in a suitable Banach space of Lp-stochastically integrable ℒ(H, E)-valued processes.
Institute of Mathematical Statistics2008
Electronic Communications in Probability
13151 - 164
yes
Van Neerven, Jan, and Jan Maas. “A Clark-Ocone Formula in UMD Banach Spaces.” <i>Electronic Communications in Probability</i>, vol. 13, Institute of Mathematical Statistics, 2008, pp. 151–64.
J. Van Neerven and J. Maas, “A Clark-Ocone formula in UMD Banach spaces,” <i>Electronic Communications in Probability</i>, vol. 13. Institute of Mathematical Statistics, pp. 151–164, 2008.
J. Van Neerven, J. Maas, Electronic Communications in Probability 13 (2008) 151–164.
Van Neerven, J., & Maas, J. (2008). A Clark-Ocone formula in UMD Banach spaces. <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics.
Van Neerven J, Maas J. 2008. A Clark-Ocone formula in UMD Banach spaces. Electronic Communications in Probability. 13, 151–164.
Van Neerven J, Maas J. A Clark-Ocone formula in UMD Banach spaces. <i>Electronic Communications in Probability</i>. 2008;13:151-164.
Van Neerven, Jan, and Jan Maas. “A Clark-Ocone Formula in UMD Banach Spaces.” <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics, 2008.
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