--- _id: '2120' abstract: - lang: eng text: 'We consider the linear stochastic Cauchy problem dX (t) =AX (t) dt +B dWH (t), t≥ 0, where A generates a C0-semigroup on a Banach space E, WH is a cylindrical Brownian motion over a Hilbert space H, and B: H → E is a bounded operator. Assuming the existence of a unique minimal invariant measure μ∞, let Lp denote the realization of the Ornstein-Uhlenbeck operator associated with this problem in Lp (E, μ∞). Under suitable assumptions concerning the invariance of the range of B under the semigroup generated by A, we prove the following domain inclusions, valid for 1 < p ≤ 2: Image omitted. Here WHk, p (E, μinfin; denotes the kth order Sobolev space of functions with Fréchet derivatives up to order k in the direction of H. No symmetry assumptions are made on L p.' acknowledgement: The authors are supported by the ‘VIDI subsidie’ 639.032.201 of the Netherlands Organization for Scientific Research (NWO) and by the Research Training Network HPRN-CT-2002-00281. author: - first_name: Jan full_name: Jan Maas id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 - first_name: Jan full_name: van Neerven, Jan M last_name: Van Neerven citation: ama: Maas J, Van Neerven J. On the domain of non-symmetric Ornstein-Uhlenbeck operators in banach spaces. Infinite Dimensional Analysis, Quantum Probability and Related Topics. 2008;11(4):603-626. doi:10.1142/S0219025708003245 apa: Maas, J., & Van Neerven, J. (2008). On the domain of non-symmetric Ornstein-Uhlenbeck operators in banach spaces. Infinite Dimensional Analysis, Quantum Probability and Related Topics. World Scientific Publishing. https://doi.org/10.1142/S0219025708003245 chicago: Maas, Jan, and Jan Van Neerven. “On the Domain of Non-Symmetric Ornstein-Uhlenbeck Operators in Banach Spaces.” Infinite Dimensional Analysis, Quantum Probability and Related Topics. World Scientific Publishing, 2008. https://doi.org/10.1142/S0219025708003245. ieee: J. Maas and J. Van Neerven, “On the domain of non-symmetric Ornstein-Uhlenbeck operators in banach spaces,” Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol. 11, no. 4. World Scientific Publishing, pp. 603–626, 2008. ista: Maas J, Van Neerven J. 2008. On the domain of non-symmetric Ornstein-Uhlenbeck operators in banach spaces. Infinite Dimensional Analysis, Quantum Probability and Related Topics. 11(4), 603–626. mla: Maas, Jan, and Jan Van Neerven. “On the Domain of Non-Symmetric Ornstein-Uhlenbeck Operators in Banach Spaces.” Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol. 11, no. 4, World Scientific Publishing, 2008, pp. 603–26, doi:10.1142/S0219025708003245. short: J. Maas, J. Van Neerven, Infinite Dimensional Analysis, Quantum Probability and Related Topics 11 (2008) 603–626. date_created: 2018-12-11T11:55:50Z date_published: 2008-12-04T00:00:00Z date_updated: 2021-01-12T06:55:26Z day: '04' doi: 10.1142/S0219025708003245 extern: 1 intvolume: ' 11' issue: '4' main_file_link: - open_access: '1' url: http://repository.tudelft.nl/view/ir/uuid:c8eca915-d38b-4827-a4d9-e89baabb43a6/ month: '12' oa: 1 page: 603 - 626 publication: Infinite Dimensional Analysis, Quantum Probability and Related Topics publication_status: published publisher: World Scientific Publishing publist_id: '4914' quality_controlled: 0 status: public title: On the domain of non-symmetric Ornstein-Uhlenbeck operators in banach spaces type: journal_article volume: 11 year: '2008' ...