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

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

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, all...

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Veröffentlicht in:Journal of evolution equations 2011-12, Vol.11 (4), p.959-993
1. Verfasser: Knäble, Florian
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Mathematics
Mathematics and Statistics
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Zusammenfassung: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.
ISSN:1424-3199
1424-3202
DOI:10.1007/s00028-011-0120-4