Monday, May 27, 2024 - 14:20 in ZiF, plenary hall
Stochastic integration with respect to cylindrical Lévy processes in Hilbert space
A talk in the SPDEvent series by
Gergely Bodó from University of Amsterdam
| Abstract: |
In this talk, we provide a complete theory of stochastic integration with respect to arbitrary cylindrical Lévy processes in Hilbert space. Since cylindrical Lévy processes do not have a semimartingale decomposition, our approach relies on a limit characterisation of Lévy characteristics and the theory of decoupled tangent sequences to introduce the notion of the stochastic integral. Our main result gives both necessary and sufficient conditions for a predictable Hilbert-Schmidt operator-valued process to be integrable with respect to an arbitrary cylindrical Lévy process in a Hilbert space. As it turns out, our integrability conditions can be explicitly expressed in terms of the cylindrical characteristics of the integrator, thus establishing a direct relationship between existence of the stochastic integral and properties of the cylindrical integrator. This is based on a joint paper with Markus Riedle from Kings's College London.
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