# A Clark-Ocone formula in UMD Banach spaces

Van Neerven J, Maas J. 2008. A Clark-Ocone formula in UMD Banach spaces. Electronic Communications in Probability. 13, 151–164.

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van Neerven, Jan M;
Maas, Jan

^{IST Austria}^{}Abstract

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.

Publishing Year

Date Published

2008-04-07

Journal Title

Electronic Communications in Probability

Acknowledgement

Research supported by ARC Discovery Grant dp0558539. 2research supported by VIDI subsidy 639.032.201 and VICI subsidy 639.033.604 of the Netherlands organisation for scientific research (nwo).

Volume

13

Page

151 - 164

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### Cite this

Van Neerven J, Maas J. A Clark-Ocone formula in UMD Banach spaces.

*Electronic Communications in Probability*. 2008;13:151-164.Van Neerven, J., & Maas, J. (2008). A Clark-Ocone formula in UMD Banach spaces.

*Electronic Communications in Probability*. Institute of Mathematical Statistics.Van Neerven, Jan, and Jan Maas. “A Clark-Ocone Formula in UMD Banach Spaces.”

*Electronic Communications in Probability*. Institute of Mathematical Statistics, 2008.J. Van Neerven and J. Maas, “A Clark-Ocone formula in UMD Banach spaces,”

*Electronic Communications in Probability*, vol. 13. Institute of Mathematical Statistics, pp. 151–164, 2008.Van Neerven, Jan, and Jan Maas. “A Clark-Ocone Formula in UMD Banach Spaces.”

*Electronic Communications in Probability*, vol. 13, Institute of Mathematical Statistics, 2008, pp. 151–64.**All files available under the following license(s):**

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