相关论文: Estimation of anisotropic Gaussian fields through …

We determine the exact Hausdorff measure functions for the range and level sets of a class of Gaussian random fields satisfying sectorial local nondeterminism and other assumptions. We also establish a Chung-type law of the iterated…

By the use of Green's second integral identity we determine the field scattered from a two-dimensional randomly rough isotropic or anisotropic Dirichlet or Neumann surface when it is illuminated by a scalar Gaussian beam. The integral…

We establish a mixed norm estimate for the Radon transform in the plane when the set of directions has fractional dimension. This estimate is used to prove a result about an exceptional set of directions connected with projections of planar…

This paper studies the problem of equivalence of Gaussian measures induced by Gaussian random fields (GRFs) with stationary increments and proves a sufficient condition for the equivalence in terms of the behavior of the spectral measures…

Isotropic covariance structures can be unreasonable for phenomena in three-dimensional spaces such as the ocean. In the ocean, the variability of the response may vary with depth, and ocean currents may lead to spatially varying anisotropy.…

This paper proposes parametric and non-parametric hypothesis testing algorithms for detecting anisotropy -- rotational variance of the covariance function in random fields. Both algorithms are based on resampling mechanisms, which enable…

We carry out numerical investigations of the perturbations in Nflation models where the mass spectrum is generated by random matrix theory. The tensor-to-scalar ratio and non-gaussianity are already known to take the single-field values,…

In this paper we study the behaviour at infinity of the Fourier transform of Radon measures supported by the images of fractal sets under an algorithmically random Brownian motion. We show that, under some computability conditions on these…

We explore a generalisation of the L\'evy fractional Brownian field on the Euclidean space based on replacing the Euclidean norm with another norm. A characterisation result for admissible norms yields a complete description of all…

In this note, we give a probabilistic interpretation of the Central Limit Theorem used for approximating isotropic Gaussians in [1].

One of the crucial aspects of density perturbations that are produced by the standard inflation scenario is that they are Gaussian where seeds produced by topological defects tend to be non-Gaussian. The three point correlation function of…

We study the problem of nonparametric estimation of the fractional derivative of unknown spectral function of Gaussian stationary sequence (time series) and show that these problems is well posed with the classical speed of convergence when…

In this paper we study the asymptotic behavior of the angular bispectrum of spherical random fields. Here, the asymptotic theory is developed in the framework of fixed-radius fields, which are observed with increasing resolution as the…

Anisotropic diffusion processes emerge in various fields such as transport in biological tissue and diffusion in liquid crystals. In such systems, the motion is described by a diffusion tensor. For a proper characterization of processes…

Spatially referenced data often have autocovariance functions with elliptical isolevel contours, a property known as geometric anisotropy. The anisotropy parameters include the tilt of the ellipse (orientation angle) with respect to a…

A method is suggested to deduce the anisotropy in neutral pions by measuring the azimuthal anisotropy of photons in ultra-relativistic nuclear collisions. The ratio of the estimated anisotropy in photons to the anisotropy in neutral pions…

Accurate ($\lesssim 1\% $) predictions for the anisotropy of the Cosmic Background Radiation (CBR) are essential for using future high-resolution ($\lesssim 1^\circ$) CBR maps to test cosmological models. In many inflationary models the…

We study rates of convergence in central limit theorems for partial sum of functionals of general stationary and non-stationary Gaussian sequences, using optimal tools from analysis on Wiener space. We apply our result to study drift…

Here we present a new non-parametric approach to density estimation and classification derived from theory in Radon transforms and image reconstruction. We start by constructing a "forward problem" in which the unknown density is mapped to…

In the course of analyzing the axiomatic principles that form the basis of statistical physics, the validity of the postulate that all the isoenergetic microstates of a closed system are equally probable was checked. This article reports…