Mathematics – Probability
Scientific paper
2011-09-09
Mathematics
Probability
Scientific paper
Let $X= \{X(t), t \in \R^N\}$ be a Gaussian random field with values in $\R^d$ defined by \[ X(t) = \big(X_1(t),..., X_d(t)\big),\qquad t \in \R^N, \] where $X_1, ..., X_d$ are independent copies of a real-valued, centered, anisotropic Gaussian random field $X_0$ which has stationary increments and the property of strong local nondeterminism. In this paper we determine the exact Hausdorff measure function for the range $X([0, 1]^N)$. We also provide a sufficient condition for a Gaussian random field with stationary increments to be strongly locally nondeterministic. This condition is given in terms of the spectral measures of the Gaussian random fields which may contain either an absolutely continuous or discrete part. This result strengthens and extends significantly the related theorems of Berman (1973, 1988), Pitt (1978) and Xiao (2007, 2009), and will have wider applicability beyond the scope of the present paper.
Luan Nana
Xiao Yimin
No associations
LandOfFree
Spectral conditions for strong local nondeterminism and exact Hausdorff measure of ranges of Gaussian random fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Spectral conditions for strong local nondeterminism and exact Hausdorff measure of ranges of Gaussian random fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spectral conditions for strong local nondeterminism and exact Hausdorff measure of ranges of Gaussian random fields will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-38198