We study a class of nonlinear stochastic partial differential equations with dissipative nonlinear drift, driven by Lévy noise. We define a Hilbert–Banach setting in which we prove existence and uniqueness of solutions under general assumptions on the drift and the Lévy 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 μ of the process, and a component which vanishes asymptotically for large times in the Lp(/mu)-sense, for all 1≤p<+∞.
|Titolo:||Invariant measures for SDEs driven by Lévy noise: A case study for dissipative nonlinear drift in infinite dimension|
DI PERSIO, Luca (Corresponding)
|Data di pubblicazione:||2017|
|Appare nelle tipologie:||01.01 Articolo in Rivista|