Renormalized Field Theory of Weakly Anisotropic Antiferromagnets under Gaussian Random Fields

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.

Sample Path Properties of Anisotropic Gaussian Random Fields

The class of anisotropic Gaussian random fields includes fractional Brownian sheets, certain operator-self-similar Gaussian random fields with stationary increments and the random string process. They arise naturally in many areas and can serve as more realistic models than fractional Brownian motion. We will discuss sample path properties of an (N, d)-fractional Brownian sheet BH = {BH(t), t ∈...

Gaussian Markov Random Fields: Theory and Applications

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...

Skew-Gaussian Random Fields

Skewness is often present in a wide range of spatial prediction problems, and modeling it in the spatial context remains a challenging problem. In this study a skew-Gaussian random field is considered. The skew-Gaussian random field is constructed by using the multivariate closed skew-normal distribution, which is a generalization of the traditional normal distribution. We present an Metropolis...