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Hölder conditions for the local times and the Hausdorff measure of the level sets of Gaussian random fields. (English) Zbl 0882.60035
Summary: Let Y(t) (t N ) 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 X(t)=(X 1 (t),,X d (t)) (t N ), 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.

MSC:
60G15Gaussian processes
60G17Sample path properties