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<p>We consider a stochastic PDE driven by a parabolic second order partial differential operator with non-constant coefficients and with a nonlinear random external forcing given by a Gaussian noise that is white in time and spatially homogeneous. We prove the existence and uniqueness of a random field solution to this SPDE. Our main result concerns the space-time sample path Hölder-continuity properties of the solution. The Hölder exponents that we obtain are essentially optimal.</p>

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Sample path regularity of non-autonomous uniformly parabolic SPDEs

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月25日

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  • Robert C. Dalang,
  • Marta Sanz-Solé

摘要

We consider a stochastic PDE driven by a parabolic second order partial differential operator with non-constant coefficients and with a nonlinear random external forcing given by a Gaussian noise that is white in time and spatially homogeneous. We prove the existence and uniqueness of a random field solution to this SPDE. Our main result concerns the space-time sample path Hölder-continuity properties of the solution. The Hölder exponents that we obtain are essentially optimal.