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Probability Theory and Related Fields

, Volume 149, Issue 1–2, pp 97–137 | Cite as

Structural properties of semilinear SPDEs driven by cylindrical stable processes

  • Enrico PriolaEmail author
  • Jerzy Zabczyk
Article

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.

Keywords

Stochastic PDEs with jumps Strong Feller property Regularity of trajectories 

Mathematics Subject Classification (2000)

60H15 60J75 47D07 35R60 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di TorinoTurinItaly
  2. 2.Instytut MatematycznyPolskiej Akademii NaukWarsawPoland

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