--- _id: '2121' abstract: - lang: eng text: 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. 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). ' author: - first_name: Jan full_name: van Neerven, Jan M last_name: Van Neerven - first_name: Jan full_name: Jan Maas id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 citation: ama: Van Neerven J, Maas J. A Clark-Ocone formula in UMD Banach spaces. Electronic Communications in Probability. 2008;13:151-164. apa: Van Neerven, J., & Maas, J. (2008). A Clark-Ocone formula in UMD Banach spaces. Electronic Communications in Probability. Institute of Mathematical Statistics. chicago: Van Neerven, Jan, and Jan Maas. “A Clark-Ocone Formula in UMD Banach Spaces.” Electronic Communications in Probability. Institute of Mathematical Statistics, 2008. ieee: 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. ista: Van Neerven J, Maas J. 2008. A Clark-Ocone formula in UMD Banach spaces. Electronic Communications in Probability. 13, 151–164. mla: 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. short: J. Van Neerven, J. Maas, Electronic Communications in Probability 13 (2008) 151–164. date_created: 2018-12-11T11:55:50Z date_published: 2008-04-07T00:00:00Z date_updated: 2021-01-12T06:55:26Z day: '07' extern: 1 intvolume: ' 13' main_file_link: - open_access: '1' url: http://arxiv.org/abs/0709.2021 month: '04' oa: 1 page: 151 - 164 publication: Electronic Communications in Probability publication_status: published publisher: Institute of Mathematical Statistics publist_id: '4915' quality_controlled: 0 status: public title: A Clark-Ocone formula in UMD Banach spaces type: journal_article volume: 13 year: '2008' ...