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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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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DOI: https://doi.org/10.1007/s00440-008-0181-7
Keywords
- Stochastic convolution
- Time homogeneous Poisson random measure and maximal regularity
- Martingale type p Banach spaces