In many problems, a specific function like h(⋅) is considered as the covariance function. Based on the asymptotic distribution of the periodogram and Euler characteristic, three methods are introduced to test the equality of the covariance function with h(⋅). Our analyses prove the accuracy...

In this paper, a random field, denoted by GTβν, is defined from the linear combination of two independent random fields, one is a Gaussian random field and the second is a student’s t random field with ν degrees of freedom scaled by β. The goal is to give the analytical expressions of the...

This paper introduces a relative structural complexity measure for the characterization of disordered surfaces. Numerical solutions of 2d+1 KPZ equation and scanning force microscopy (SFM) patterns of porous silicon samples are analyzed using this methodology. The results and phenomenological...

We prove a functional central limit theorem for the Hausdorff measure of level sets generated by a smooth Gaussian random field.