{"year":"2008","day":"04","type":"journal_article","status":"public","author":[{"orcid":"0000-0002-0845-1338","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","last_name":"Maas","full_name":"Jan Maas"},{"last_name":"Van Neerven","full_name":"van Neerven, Jan M","first_name":"Jan"}],"date_published":"2008-12-04T00:00:00Z","main_file_link":[{"url":"http://repository.tudelft.nl/view/ir/uuid:c8eca915-d38b-4827-a4d9-e89baabb43a6/","open_access":"1"}],"title":"On the domain of non-symmetric Ornstein-Uhlenbeck operators in banach spaces","_id":"2120","quality_controlled":0,"publication":"Infinite Dimensional Analysis, Quantum Probability and Related Topics","date_created":"2018-12-11T11:55:50Z","month":"12","date_updated":"2021-01-12T06:55:26Z","page":"603 - 626","volume":11,"publist_id":"4914","abstract":[{"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 &lt; 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.","lang":"eng"}],"publisher":"World Scientific Publishing","extern":1,"issue":"4","intvolume":"        11","doi":"10.1142/S0219025708003245","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.","oa":1,"publication_status":"published","citation":{"ama":"Maas J, Van Neerven J. On the domain of non-symmetric Ornstein-Uhlenbeck operators in banach spaces. <i>Infinite Dimensional Analysis, Quantum Probability and Related Topics</i>. 2008;11(4):603-626. doi:<a href=\"https://doi.org/10.1142/S0219025708003245\">10.1142/S0219025708003245</a>","ieee":"J. Maas and J. Van Neerven, “On the domain of non-symmetric Ornstein-Uhlenbeck operators in banach spaces,” <i>Infinite Dimensional Analysis, Quantum Probability and Related Topics</i>, vol. 11, no. 4. World Scientific Publishing, pp. 603–626, 2008.","chicago":"Maas, Jan, and Jan Van Neerven. “On the Domain of Non-Symmetric Ornstein-Uhlenbeck Operators in Banach Spaces.” <i>Infinite Dimensional Analysis, Quantum Probability and Related Topics</i>. World Scientific Publishing, 2008. <a href=\"https://doi.org/10.1142/S0219025708003245\">https://doi.org/10.1142/S0219025708003245</a>.","short":"J. Maas, J. Van Neerven, Infinite Dimensional Analysis, Quantum Probability and Related Topics 11 (2008) 603–626.","apa":"Maas, J., &#38; Van Neerven, J. (2008). On the domain of non-symmetric Ornstein-Uhlenbeck operators in banach spaces. <i>Infinite Dimensional Analysis, Quantum Probability and Related Topics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0219025708003245\">https://doi.org/10.1142/S0219025708003245</a>","mla":"Maas, Jan, and Jan Van Neerven. “On the Domain of Non-Symmetric Ornstein-Uhlenbeck Operators in Banach Spaces.” <i>Infinite Dimensional Analysis, Quantum Probability and Related Topics</i>, vol. 11, no. 4, World Scientific Publishing, 2008, pp. 603–26, doi:<a href=\"https://doi.org/10.1142/S0219025708003245\">10.1142/S0219025708003245</a>.","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."}}