Journal of Evolution Equations

, Volume 11, Issue 4, pp 959–993 | Cite as

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

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.

Keywords

Invariant Measure Mild Solution Harnack Inequality Evolution Family Strong Continuity 
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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Universität BielefeldFakultät für MathematikBielefeldGermany

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