We study a class of nonlinear stochastic partial differential equations with dissipative nonlinear drift, driven by Levy noise. We define a Hilbert-Banach setting in which we prove existence and uniqueness of solutions under general assumptions on the drift and the Levy noise. We then prove a decomposition of the solution process into a stationary component, the law of which is identified with the unique invariant probability measure mu of the process, and a component which vanishes asymptotically for large times in the L-P (mu)-sense, for all 1 <= p < + infinity.

Invariant measures for sdes driven by lévy noise: A case study for dissipative nonlinear drift in infinite dimension

MASTROGIACOMO, ELISA;
2017-01-01

Abstract

We study a class of nonlinear stochastic partial differential equations with dissipative nonlinear drift, driven by Levy noise. We define a Hilbert-Banach setting in which we prove existence and uniqueness of solutions under general assumptions on the drift and the Levy noise. We then prove a decomposition of the solution process into a stationary component, the law of which is identified with the unique invariant probability measure mu of the process, and a component which vanishes asymptotically for large times in the L-P (mu)-sense, for all 1 <= p < + infinity.
2017
Dissipative nonlinear drift; Invariant measure; Lévy noise; Nonlinear SPDEs;
Albeverio, S.; Di Persio, L.; Mastrogiacomo, Elisa; Smii, B.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2060244
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