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Maximal regularity for stochastic convolutions driven by Lévy processes
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  • Published: 03 December 2008

Maximal regularity for stochastic convolutions driven by Lévy processes

  • Zdzisław Brzeźniak1 &
  • Erika Hausenblas2 

Probability Theory and Related Fields volume 145, pages 615–637 (2009)Cite this article

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Abstract

We generalize the maximal regularity result from Da Prato and Lunardi (Atti Accad Naz Lincei Cl Sci Fis Mat Natur Rend Lincei (9) Mat Appl 9(1):25–29, 1998) to stochastic convolutions driven by time homogenous Poisson random measures and cylindrical infinite dimensional Wiener processes.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of York, Heslington, York, YO10 5DD, UK

    Zdzisław Brzeźniak

  2. Department of Mathematics, University of Salzburg, Hellbrunnerstr. 34, 5020, Salzburg, Austria

    Erika Hausenblas

Authors
  1. Zdzisław Brzeźniak
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  2. Erika Hausenblas
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Corresponding author

Correspondence to Zdzisław Brzeźniak.

Additional information

The research of both authors was supported by a grant P17273 of the Austrian Science Foundation. The research of the first named author was supported by an ARC Discovery grant DP0663153. The research on this paper was initiated during a visit of both authors to the Centro di Ricerca Matematica Ennio de Giorgi in Pisa (Italy), in July 2006. Both authors would like to thank Ben Gołdys, Anna Chojnowska-Michalik and Martin Ondrejat for comments and suggestions and Anna Chojnowska-Michalik also for very careful reading of the manuscript.

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Brzeźniak, Z., Hausenblas, E. Maximal regularity for stochastic convolutions driven by Lévy processes. Probab. Theory Relat. Fields 145, 615–637 (2009). https://doi.org/10.1007/s00440-008-0181-7

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  • Received: 17 August 2007

  • Revised: 08 September 2008

  • Published: 03 December 2008

  • Issue Date: November 2009

  • DOI: https://doi.org/10.1007/s00440-008-0181-7

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Keywords

  • Stochastic convolution
  • Time homogeneous Poisson random measure and maximal regularity
  • Martingale type p Banach spaces

Mathematics Subject Classification (2000)

  • 60H15
  • 60J75
  • 60G57
  • 60H05
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