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Ornstein–Uhlenbeck equations with time-dependent coefficients and Lévy noise in finite and infinite dimensions

Journal of Evolution Equations volume 11, pages 959–993 (2011)Cite this article

Abstract

We solve a time-dependent linear SPDE with additive Lévy noise in the mild and weak sense. Existence of a generalized invariant measure for the associated transition semigroup is established and the generator is studied on the corresponding L 2-space. The square field operator is characterized, allowing to derive a Poincaré and a Harnack inequality.

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  1. Universität Bielefeld, Fakultät für Mathematik, Universitätsstraße 25, 33615, Bielefeld, Germany

    Florian Knäble

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  1. Florian Knäble
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Correspondence to Florian Knäble.

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Knäble, F. Ornstein–Uhlenbeck equations with time-dependent coefficients and Lévy noise in finite and infinite dimensions. J. Evol. Equ. 11, 959–993 (2011). https://doi.org/10.1007/s00028-011-0120-4

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  • DOI: https://doi.org/10.1007/s00028-011-0120-4

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