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