A Note on time regularity of generalized Ornstein-Uhlenbeck processes with cylindrical stable noise

Liu, Yong<sup>*</sup>; Zhai, Jianliang

doi:10.1016/j.crma.2011.11.017

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A Note on time regularity of generalized Ornstein-Uhlenbeck processes with cylindrical stable noise

作者：Liu, Yong^*; Zhai, Jianliang

来源：Comptes Rendus Mathematique, 2012, 350(1-2): 97-100.

DOI：10.1016/j.crma.2011.11.017

摘要

A necessary and sufficient condition of cadlag modification of Ornstein-Uhlenbeck process with cylindrical stable noise in a Hilbert space is given in this Note. Applying this result. some questions in Time irregularity of generalized Ornstein-Uhlenbeck processes [C. R. Acad. Sci. Paris, Ser. I 348 (2010) 273-276] and Structural properties of semilinear SPDEs driven by cylindrical stable process [Probab. Theory Related Fields 149 (2011) 97-137] are answered.