Potential Analysis

, Volume 32, Issue 2, pp 153–188 | Cite as

Regularity of Ornstein–Uhlenbeck Processes Driven by a Lévy White Noise

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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.

Keywords

Lévy white noise Subordinator process Langevin equation Space regularity Stochastic heat equation Non-cádlág trajectories Stochastic Burgers equation 

Mathematics Subject Classifications (2000)

60H15 60J75 60G57 60H05 
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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of MathematicsThe University of YorkHeslingtonUK
  2. 2.Institute of MathematicsPolish Academy of SciencesWarsawPoland

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