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Martingale-valued measures, Ornstein-Uhlenbeck processes with jumps and operator self-decomposability in Hilbert space

Applebaum, D. (2006) Martingale-valued measures, Ornstein-Uhlenbeck processes with jumps and operator self-decomposability in Hilbert space. In: In Memoriam Paul-André Meyer. Lecture Notes in Mathematics, 1874 . Springer Berlin / Heidelberg , pp. 171-196. ISBN 978-3-540-30994-9

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Abstract

We investigate a class of Hilbert space valued martingale-valued measures whose covariance structure is determined by a trace class positive operator valued measure. The paradigm example is the martingale part of a Levy process. We develop both weak and strong stochastic integration with respect to such martingale-valued measures. As an application, we investigate the stochastic convolution of a C0-semigroup with a Levy process and the associated Ornstein-Uhlenbeck process. We give an in¯nite dimensional generalisation of the concept of operator self-decomposability and conditions for random variables of this type to be embedded into a stationary Ornstein-Uhlenbeck process.

Item Type: Book Section
Copyright, Publisher and Additional Information: © 2006 Springer. This is an author produced version of a book chapter subsequently published in, In Memoriam Paul-André Meyer . Uploaded in accordance with the publisher's self-archiving policy.
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 13:44
Last Modified: 08 Feb 2013 16:59
Published Version: http://dx.doi.org/10.1007/978-3-540-35513-7_14
Status: Published
Publisher: Springer Berlin / Heidelberg
Refereed: Yes
Identification Number: 10.1007/978-3-540-35513-7_14
URI: http://eprints.whiterose.ac.uk/id/eprint/9796

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