Applebaum, D. (2007) On the infinitesimal generators of Ornstein–Uhlenbeck processes with jumps in Hilbert space. Potential Analysis, 26 (1). pp. 79-100. ISSN 0926-2601
Abstract
We study Hilbert space valued Ornstein–Uhlenbeck processes (Y(t), t ≥ 0) which arise as weak solutions of stochastic differential equations of the type dY = JY + CdX(t) where J generates a C 0 semigroup in the Hilbert space H, C is a bounded operator and (X(t), t ≥ 0) is an H-valued Lévy process. The associated Markov semigroup is of generalised Mehler type. We discuss an analogue of the Feller property for this semigroup and explicitly compute the action of its generator on a suitable space of twice-differentiable functions. We also compare the properties of the semigroup and its generator with respect to the mixed topology and the topology of uniform convergence on compacta.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2007 Springer. This is an author produced version of a paper subsequently published in Potential Analysis. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | H-valued Lévy process; Ornstein–Uhlenbeck process; generalised Mehler semigroup; auxiliary semigroup; operator-selfdecomposability; quasi-locally equicontinuous semigroup; pseudo-Feller property; mixed topology; cylinder function; Kolmogorov–Lévy operator |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Miss Anthea Tucker |
Date Deposited: | 30 Sep 2009 13:20 |
Last Modified: | 16 Nov 2015 11:48 |
Published Version: | http://dx.doi.org/10.1007/s11118-006-9028-y |
Status: | Published |
Publisher: | Springer Verlag |
Refereed: | Yes |
Identification Number: | 10.1007/s11118-006-9028-y |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:9800 |