Computer-aided modelling is one of the most effective means of getting to the root of a natural phenomenon and of predicting the consequences of human impact on the environment. General methods of numerical modelling of random processes have been effectively developed and the area of applications has rapidly expanded in recent years. This book deals with the development and investigation of numerical methods for simulation of random processes and fields. The book opens with a description of scalar and vector-valued Gaussian models, followed by non-Gaussian models. Furthermore, issues of convergence of approximate models of random fields are studied. The last part of this book is devoted to applications of stochastic modelling, in which new application areas such as simulation of meteorological processes and fields, sea surface undulation, and stochastic structure of clouds, are presented.

Spectral models were developed in the 1970s and have appeared to be very promising for various applications. Nowadays, spectral models are extensively used for stochastic simulation in atmosphere and ocean optics, turbulence theory, analysis of pollution transport for porous media, astrophysics, and other fields of science. The spectral models presented in this monograph represent a new class of numerical methods aimed at simulation of random processes and fields. The book is divided into four chapters, which deal with scalar spectral models and some of their applications, vector-valued spectral models, convergence of spectral models, and problems of optimisation and convergence for functional Monte Carlo methods. Furthermore, the monograph includes four appendices, in which auxiliary information is presented and additional problems are discussed. The book will be of value and interest to experts in Monte Carlo methods, as well as to those interested in the theory and applications of stochastic simulation.