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Stochastic integration with respect to cylindrical Levy processes in Hilbert spaces: an L2 approach

Research output: Contribution to journalArticlepeer-review

Original languageEnglish
Article number1450008
Number of pages19
JournalINFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS
Volume17
Issue number1
DOIs
Published26 Mar 2014

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  • 1207.2634v1

    1207.2634v1.pdf, 188 KB, application/pdf

    Uploaded date:21 Jul 2015

    Version:Submitted manuscript

King's Authors

Abstract

In this work stochastic integration with respect to cylindrical Levy processes with weak second moments is introduced. It is well known that a deterministic Hilbert-Schmidt operator radonifies a cylindrical random variable, i.e. it maps a cylindrical random variable to a classical Hilbert space valued random variable. Our approach is based on a generalisation of this result to the radonification of the cylindrical increments of a cylindrical Levy process by random Hilbert-Schmidt operators. This generalisation enables us to introduce a Hilbert space valued random variable as the stochastic integral of a predictable stochastic process with respect to a cylindrical Levy process. We finish this work by deriving an Ito isometry and by considering shortly stochastic partial differential equations driven by cylindrical Levy processes.

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