Gaussian fields and Gaussian sheets with generalized Cauchy covariance structure

TL;DR

This paper investigates Gaussian fields and sheets with generalized Cauchy covariance, analyzing their properties, spectral densities, and self-similar transformations to deepen understanding of their structure and behavior.

Contribution

It introduces and studies the properties of GFGCC and GSGCC, including their spectral densities and self-similar transformations, expanding the theoretical framework of Gaussian random fields.

Findings

Analysis of spectral densities of GFGCC and GSGCC

Characterization of asymptotic properties of these fields

Identification of self-similar processes via Lamperti transformation

Abstract

Two types of Gaussian processes, namely the Gaussian field with generalized Cauchy covariance (GFGCC) and the Gaussian sheet with generalized Cauchy covariance (GSGCC) are considered. Some of the basic properties and the asymptotic properties of the spectral densities of these random fields are studied. The associated self-similar random fields obtained by applying the Lamperti transformation to GFGCC and GSGCC are studied.