Simulation and estimation of operator scaling stable random fields

Operator-scaling stable random fields are stochastic models which can describe spacial dependencies. Thereby dependencies of different intensities and in different, not necessarily orthogonal, directions are allowed, resulting in anisotropic fields which are used, e.g. in hydrology to represent porous media, or to describe fractal surfaces in physics. In the year 2006, H. Biermé, M. M. Meerschaert and H.-P. Scheffler presented models for operator-scaling stable random fields in harmonizable and in moving average representation, and showed some important properties of these fields.
In order to use these fields for practical application, procedures for their numeric simulation are needed, and also methods for the statistical analysis (e.g. parameter estimation) of observed realizations of OSSRFs. The present thesis presents numeric approximations of OSSRFs and examines their deviation from the original OSSRFs. Algorithms for the calculation of these approximations have been also developed and are described in the thesis. For the cases of two- and three-dimensional fields, which are relevant for practical applications, these algorithms for the simulation of OSSRFs have been implemented in the programming languages Matlab and Java. Finally, we present also a method for the estimation of several parameters of a two-dimensional harmonizable OSSRF, and its implementation in Matlab.