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<p>Let <i>X</i> = {<i>X</i>(<i>t</i>), <i>t</i> ∈ ∝<sup><i>N</i></sup>} be a centered space-time anisotropic Gaussian random field with values in ℝ<sup><i>d</i></sup>. Under some general conditions, the existence, joint continuity and Hölder conditions of higher-order derivative of local times of <i>X</i> are studied. Moreover, we obtain the uniform Hausdorff dimension of the inverse images of <i>X</i>. The existing results of Gaussian random fields are extended to space-time anisotropic Gaussian random fields with approximate independent components.</p>

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Derivatives of Local Times and Hausdorff Dimension of Inverse Images of Space-time Anisotropic Gaussian Random Fields

  • 期刊论文

  • 发表日期：

    2026年1月15日

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  • Peng Xu,
  • Zhenlong Chen

摘要

Let X = {X(t), t ∈ ∝N} be a centered space-time anisotropic Gaussian random field with values in ℝd. Under some general conditions, the existence, joint continuity and Hölder conditions of higher-order derivative of local times of X are studied. Moreover, we obtain the uniform Hausdorff dimension of the inverse images of X. The existing results of Gaussian random fields are extended to space-time anisotropic Gaussian random fields with approximate independent components.