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Hölder conditions for the local times and the Hausdorff measure of the level sets of Gaussian random fields
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  • Published: September 1997

Hölder conditions for the local times and the Hausdorff measure of the level sets of Gaussian random fields

  • Yimin Xiao1 

Probability Theory and Related Fields volume 109, pages 129–157 (1997)Cite this article

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Summary.

Let Y(t) (t∈ℝN) be a real-valued, strongly locally nondeterministic Gaussian random field with stationary increments and Y(0)=0. Consider the (N,d) Gaussian random field defined by

where X 1,…,X d are independent copies of Y. The local and global Hölder conditions in the set variable for the local time of X(t) are established and the exact Hausdorff measure of the level set X −1(x) is evaluated.

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Authors and Affiliations

  1. Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, USA (xiao@math.utah.edu), , , , , , US

    Yimin Xiao

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  1. Yimin Xiao
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Received: 28 October 1996 / In revised form: 5 May 1997

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Cite this article

Xiao, Y. Hölder conditions for the local times and the Hausdorff measure of the level sets of Gaussian random fields. Probab Theory Relat Fields 109, 129–157 (1997). https://doi.org/10.1007/s004400050128

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  • Issue Date: September 1997

  • DOI: https://doi.org/10.1007/s004400050128

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  • Key words: Local times
  • Gaussian random fields
  • Fractional Brownian motion
  • Level sets
  • Hausdorff measure
  • Mathematics Subject Classification (1991): Primary 60G15
  • 60G17
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