---
_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'
...