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

By D. Applebaum

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

Publisher: Springer Berlin / Heidelberg
Year: 2006
OAI identifier: oai:eprints.whiterose.ac.uk:9796

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