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

A necessary and sufficient condition of càdlàg 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.

RésuméUne condition nécessaire et suffisante de la modification càdlàg des processus dʼOrnstein–Uhlenbeck avec bruit stables cylindriques dans un éspace Hilbert est montré dans cette Note. En appliquant ce résultat, quelques questions dans Time irregularity of generalized Ornstein–Uhlenbeck processes [C. R. Acad. Sci. Paris, Ser. I 348 (2010) 273–276] et Structural properties of semilinear SPDEs driven by cylindrical stable process [Probab. Theory Related Fields 149 (2011) 97–137] sont répondues.