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Regularity of Ornstein-Uhlenbeck processes driven by a Lévy white noise. (English) Zbl 1187.60048
Authors’ abstract: The paper is concerned with spatial and time regularity of solutions to linear stochastic evolution equation perturbed by Lévy white noise “obtained by subordination of a Gaussian white noise”. Sufficient conditions for spatial continuity are derived. It is also shown that solutions do not have in general cádlág modifications. General results are applied to equations with fractional Laplacian. Applications to Burgers stochastic equations are considered as well.
60H15Stochastic partial differential equations
60J75Jump processes
60G57Random measures
60H05Stochastic integrals
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