On the domain of non-symmetric Ornstein-Uhlenbeck operators in banach spaces

J. Maas, J. Van Neerven, Infinite Dimensional Analysis, Quantum Probability and Related Topics 11 (2008) 603–626.


Journal Article | Published
Author
Maas, JanIST Austria ; van Neerven, Jan M
Abstract
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.
Publishing Year
Date Published
2008-12-04
Journal Title
Infinite Dimensional Analysis, Quantum Probability and Related Topics
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.
Volume
11
Issue
4
Page
603 - 626
IST-REx-ID

Cite this

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
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. https://doi.org/10.1142/S0219025708003245
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 11, no. 4 (2008): 603–26. https://doi.org/10.1142/S0219025708003245.
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, pp. 603–626, 2008.
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.
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.
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