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Structural properties of semilinear SPDEs driven by cylindrical stable processes
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  • Published: 16 September 2009

Structural properties of semilinear SPDEs driven by cylindrical stable processes

  • Enrico Priola1 &
  • Jerzy Zabczyk2 

Probability Theory and Related Fields volume 149, pages 97–137 (2011)Cite this article

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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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Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123, Turin, Italy

    Enrico Priola

  2. Instytut Matematyczny, Polskiej Akademii Nauk, ul.Sniadeckich 8, 00-950, Warsaw, Poland

    Jerzy Zabczyk

Authors
  1. Enrico Priola
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  2. Jerzy Zabczyk
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Corresponding author

Correspondence to Enrico Priola.

Additional information

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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  • Received: 24 November 2008

  • Revised: 03 August 2009

  • Published: 16 September 2009

  • Issue Date: February 2011

  • DOI: https://doi.org/10.1007/s00440-009-0243-5

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Keywords

  • Stochastic PDEs with jumps
  • Strong Feller property
  • Regularity of trajectories

Mathematics Subject Classification (2000)

  • 60H15
  • 60J75
  • 47D07
  • 35R60
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