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Ornstein-Uhlenbeck Processes Driven by Cylindrical Lévy Processes

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Abstract

In this article we introduce a theory of integration for deterministic, operator-valued integrands with respect to cylindrical Lévy processes in separable Banach spaces. Here, a cylindrical Lévy process is understood in the classical framework of cylindrical random variables and cylindrical measures, and thus, it can be considered as a natural generalisation of cylindrical Wiener processes or white noises. Depending on the underlying Banach space, we provide necessary and/or sufficient conditions for a function to be integrable. In the last part, the developed theory is applied to define Ornstein-Uhlenbeck processes driven by cylindrical Lévy processes and several examples are considered.

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Authors and Affiliations

  1. Department of Mathematics, King’s College London, London, WC2R 2LS, UK

    Markus Riedle

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  1. Markus Riedle
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Correspondence to Markus Riedle.

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The author acknowledges the EPSRC grant EP/I036990/1

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Riedle, M. Ornstein-Uhlenbeck Processes Driven by Cylindrical Lévy Processes. Potential Anal 42, 809–838 (2015). https://doi.org/10.1007/s11118-014-9458-x

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