Author(s):

Maas, Jan; van Neerven, Jan M

Article Title: 
On the domain of nonsymmetric OrnsteinUhlenbeck 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 C0semigroup 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 OrnsteinUhlenbeck 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:

02190257

Publisher:

World Scientific Publishing

Date Published:

20081204

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 HPRNCT200200281.

URL: 

DOI: 
10.1142/S0219025708003245

Open access: 
yes (repository) 