---
_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'
...