Abstract
We consider a class of semilinear stochastic evolution equations driven by an additive cylindrical stable noise. We investigate structural properties of the solutions like Markov, irreducibility, stochastic continuity, Feller and strong Feller properties, and study integrability of trajectories. The obtained results are applied to semilinear stochastic heat equations with Dirichlet boundary conditions and bounded and Lipschitz nonlinearities.
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Research of E. Priola was supported by the M.I.U.R. research projects Prin 2004 and 2006 “Kolmogorov equations”.
Research of E. Priola and J. Zabczyk was supported by the Polish Ministry of Science and Education project 1PO 3A 034 29 “Stochastic evolution equations with Lévy noise” and by the European Grant “SPADE2”.
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Priola, E., Zabczyk, J. Structural properties of semilinear SPDEs driven by cylindrical stable processes. Probab. Theory Relat. Fields 149, 97–137 (2011). https://doi.org/10.1007/s00440-009-0243-5
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DOI: https://doi.org/10.1007/s00440-009-0243-5