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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Received: 28 October 1996 / In revised form: 5 May 1997
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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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DOI: https://doi.org/10.1007/s004400050128
- Key words: Local times
- Gaussian random fields
- Fractional Brownian motion
- Level sets
- Hausdorff measure
- Mathematics Subject Classification (1991): Primary 60G15
- 60G17