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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.

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Authors and Affiliations

  1. Department of Mathematics, The University of York, Heslington, York, YO10 5DD, UK

    Zdzisław Brzeźniak

  2. Institute of Mathematics, Polish Academy of Sciences, 00-950, Warsaw, Poland

    Jerzy Zabczyk

Authors
  1. Zdzisław Brzeźniak
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  2. Jerzy Zabczyk
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Correspondence to Zdzisław Brzeźniak.

Additional information

Supported by the Polish Ministry of Science and Education project 1PO 3A 034 29 ‘‘Stochastic evolution equations with Lévy noise’’ and by EC FP6 Marie Curie ToK programme SPADE2. Research of the first named author was also supported by an EPSRC grant number EP/E01822X/1.

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Brzeźniak, Z., Zabczyk, J. Regularity of Ornstein–Uhlenbeck Processes Driven by a Lévy White Noise. Potential Anal 32, 153–188 (2010). https://doi.org/10.1007/s11118-009-9149-1

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  • DOI: https://doi.org/10.1007/s11118-009-9149-1

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