Anisotropic Gaussian random fields: criteria for hitting probabilities and applications

Hitting Probabilities and the Hausdorff Dimension of the Inverse Images of Anisotropic Gaussian Random Fields

Let X = {X(t), t ∈ RN} be a Gaussian random field with values in R defined by X(t) = ( X1(t), . . . , Xd(t) ) , where X1, . . . , Xd are independent copies of a centered Gaussian random field X0. Under certain general conditions on X0, we study the hitting probabilities of X and determine the Hausdorff dimension of the inverse image X−1(F ), where F ⊆ R is a non-random Borel set. The class of G...

Hitting Estimates for Gaussian Random Fields

We provide estimates for the probability that a continuous, stationary Gaussian random eld hits a small ball. Our estimates are used to study the sample functions of (N, d) Brownian sheet and its corresponding integrated process.

Packing Dimension Results for Anisotropic Gaussian Random Fields

Let X = {X(t), t ∈ RN} be a Gaussian random field with values in Rd defined by X(t) = ( X1(t), . . . , Xd(t) ) , ∀ t ∈ R , where X1, . . . , Xd are independent copies of a centered real-valued Gaussian random field X0. We consider the case when X0 is anisotropic and study the packing dimension of the range X(E), where E ⊆ RN is a Borel set. For this purpose we extend the original notion of pack...

Gaussian Markov Random Fields: Theory and Applications

On Local times of Anisotropic Gaussian Random Fields

The joint continuity of local times is proved for a large class of anisotropic Gaussian random fields. Sharp local and global Hölder conditions for the local times under an anisotropic metric are established. These results are useful for studying sample path and fractal properties of the Gaussian fields.