Regularity of Ornstein-Uhlenbeck processes driven by a L{é}vy white noise

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 \cadlag modifications. General results are applied to equations with fractional Laplacian. Applications to Burgers stochastic equations are considered as well.

This is an updated version of the same paper. In fact, it has already been published

Cited by in corpus (6)

• Stochastic Reaction-diffusion Equations Driven by Jump Processes
• Path properties of the solution to the stochastic heat equation with Lévy noise
• Stochastic integration in Hilbert spaces with respect to cylindrical martingale-valued measures
• Modelling Levy space-time white noises
• Ergodicity bounds for stable Ornstein-Uhlenbeck systems in Wasserstein distance with applications to cutoff stability
• The cutoff phenomenon for the stochastic heat and the wave equation subject to small Lévy noise