SPDEs with rough noise in space: Hölder continuity of the solution

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Abstract

© 2016 Elsevier B.V. We consider the stochastic wave and heat equations with affine multiplicative Gaussian noise which is white in time and behaves in space like the fractional Brownian motion with index H∈(14,12). The existence and uniqueness of the solution to these equations has been proved recently by the authors. In the present note we show that these solutions have modifications which are Hölder continuous in space of order smaller than H, and Hölder continuous in time of order smaller than γ, where γ=H for the wave equation and γ=H/2 for the heat equation.
Original languageEnglish
Pages (from-to)310-316
JournalStatistics and Probability Letters
Volume119
DOIs
Publication statusPublished - 1 Dec 2016

Keywords

  • Fractional noise
  • Hölder continuous paths
  • Stochastic heat equation
  • Stochastic wave equation

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