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


Author(s): Maas, Jan; van Neerven, Jan M
Article Title: On the domain of non-symmetric Ornstein-Uhlenbeck operators in banach spaces
Affiliation
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.
Keywords: Nonsymmetric Ornstein–Uhlenbeck operators; domain inclusions; invariant measures; Cauchy semigroup; H∞-calculus
Journal Title: Infinite Dimensional Analysis, Quantum Probability and Related Topics
Volume: 11
Issue 4
ISSN: 0219-0257
Publisher: World Scientific Publishing  
Date Published: 2008-12-04
Start Page: 603
End Page: 626
Sponsor: 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.
URL:
DOI: 10.1142/S0219025708003245
Open access: yes (repository)
IST Austria Authors
  1. Jan Maas
    28 Maas