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Stochastic integration with respect to cylindrical Lévy processes

Research output: Contribution to journalArticlepeer-review

Markus Riedle, Adam Jakubowski

Original languageEnglish
Pages (from-to)4273-4306
Number of pages34
JournalANNALS OF PROBABILITY
Volume45
Issue number6B
Early online date12 Dec 2017
DOIs
Accepted/In press22 Oct 2016
E-pub ahead of print12 Dec 2017
Published2017

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Abstract

A cylindrical Lévy process does not enjoy a cylindrical version of the
semimartingale decomposition which results in the need to develop a completely novel approach to stochastic integration. In this work, we introduce a stochastic integral for random integrands with respect to cylindrical Lévy processes in Hilbert spaces. The space of admissible integrands consists of càglàd, adapted stochastic processes with values in the space of Hilbert-Schmidt operators. Neither the integrands nor the integrator is required to satisfy any moment or boundedness condition. The integral process is characterised as an adapted, Hilbert space valued semimartingale with càdlàg trajectories.

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