Explicit constructions of operator scaling Gaussian fields

We propose an explicit way to generate a large class of Operator scaling Gaussian random fields (OSGRF). Such fields are anisotropic generalizations of selfsimilar fields. More specifically, we are able to construct any Gaussian field belonging to this class with given Hurst index and exponent. Our construction provides - for simulations of texture as well as for detection of anisotropies in an image - a large class of models with controlled anisotropic geometries and structures

Extrapolation of Stationary Random Fields

We introduce basic statistical methods for the extrapolation of stationary random fields. For square integrable fields, we set out basics of the kriging extrapolation techniques. For (non--Gaussian) stable fields, which are known to be heavy tailed, we describe further extrapolation methods and discuss their properties. Two of them can be seen as direct generalizations of kriging.Comment: 52 pages, 25 figures. This is a review article, though Section 4 of the article contains new results on the weak consistency of the extrapolation methods as well as new extrapolation methods for $\alpha$-stable fields with $0<\alpha\leq 1

Modeling the galactic diffuse gamma-ray emission

The diffuse gamma-ray emission in our Galaxy is produced by highly energetic electrons interacting mainly with radiation fields through inverse Compton scattering or in interactions with interstellar matter through Bremsstrahlung. Furthermore, protons also interact with the interstellar matter and produce gamma-rays through the production of pion particles and their subsequent decay. The energy range of gamma-ray emission covers the domain from a few MeV (1 MeV = 106 eV) up to energies > 100 TeV (1 TeV = 1012 eV). In this work a model to predict the diffuse gamma-ray emission is presented. The general idea of this model is to simulate a population of galactic sources, which accelerate protons and electrons, distributed according to the populations of supernova remnants and pulsars at radio wavelengths. Through the previously mentioned interaction processes, the diffuse gamma-ray emission spectrum can be predicted for different regions of the Galaxy. The goal of this thesis is to produce the spectrum of diffuse gamma-ray emission for the two different regions of the Galaxy at l=344 longitude, b=0 latitude and at l=344 longitude, b=4 latitude

Tauberian and Abelian theorems for long-range dependent random fields

This paper surveys Abelian and Tauberian theorems for long-range dependent random fields. We describe a framework for asymptotic behaviour of covariance functions or variances of averaged functionals of random fields at infinity and spectral densities at zero. The use of the theorems and their limitations are demonstrated through applications to some new and less-known examples of covariance functions of long-range dependent random fields.Comment: Will appear in Methodology and Computing in Applied Probability. 26 pages, 10 figures. The final publication is available at link.springer.com. DOI: 10.1007/s11009-012-9276-