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abstract:
The talk is devoted to time and spatial regularity of Ornstein-Uhlenbeck processes with L\'{e}vy perturbations. Extensions to solutions of non-linear equations will be discussed as well. The following topics will be covered: Cylindrical L\'{e}vy processes; Examples of time irregular solutions; Stochastic continuity and strong Feller properties of solutions; Spatial regularity for solutions of equations with subordinated Wiener process.
The presentation is based on joint research with Z. Brzezniak and E. Priola.
References
Z. Brzezniak and J. Zabczyk, Regularity of Ornstein-Uhlenbeck processes driven by a L\'{e}vy white noise, Potential Analysis (2010), to appear
E. Priola and J. Zabczyk, Structural properties of semilinear spdes driven by cylindrical stable processes, PTRF (2010), to appear |
