Numerical Modelling of Random Processes and Fields: Algorithms and Applications

01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information. 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.

Table of Contents:
Preface STATISTICAL SIMULATION OF DISCRETE GAUSSIAN PROCESSES AND FIELDS WITH A GIVEN CORRELATION STRUCTURE Method of conditional expectations Simulation of the Gaussian vectors with correlation matrix of stationary type Regularization of the algorithm Simulation of autoregressive processes with a desired correlation structure Simulation of stationary Gaussian vector sequences and discrete spatial fields with a given correlation structure Simulation of vector autoregressive sequences Linear transformation method Special algorithms for simulation of homogeneous isotropic discrete Gaussian fields SPECTRAL MODELS OF GAUSSIAN RANDOM FIELDS Construction of spectral models Spectral models of homogeneous vector fields NUMERICAL MODELS OF NON-GAUSSIAN PROCESSES AND FIELDS Consistency conditions of marginal distributions and covariance function Method of inverse distribution functions Models based on stochastic differential equations ''Repetition'' method for simulation of random vectors and processes Method for simulation of random processes and fields on point flows Randomized models of non-Gaussian discrete processes Combined models of non-Gaussian process and fields Numerical models of certain classes of non-Gaussian homogeneous processes and fields CONVERGENCE OF NUMERICAL MODELS OF RANDOM FIELDS IN MONTE CARLO METHOD Introduction Weak convergence of probability measures and random functions Conditions of weak convergence in spaces C and C Convergence of spectral models of the Gaussian homogeneous fields Convergence of one class of non-Gaussian models Remark on allowance for bias of estimates constructed by approximate models Appendix to Chapter 4. Some applications of the Jane-Marcus central limit theorem in statistical simulation SIMULATION OF RANDOM FIELDS IN STOCHASTIC PROBLEMS OF THE ATMOSPHERE--OCEAN OPTICS Numerical modelling of stochastic structure of cumulus clouds for investigation of the solar radiation transfer in the atmosphere Simulation of the undulated sea surface and study of its optical properties by Monte Carlo method HYDROMETEOROLOGICAL APPLICATIONS OF STATISTICAL SIMULATION METHODS Influence of uncertainty in initial data on forecasting accuracy On accuracy of temperature vertical profiles expansion into a series by eigenvectors of sampling covariance matrix Investigation of some features of excursions of air temperature time series Probabilistic models of dry and rainy days time series Probability properties of precipitation amount Approximation of empirical probability distribution of daily rainy precipitation sums Probabilistic model of non-stationary vector sequences in applications to some joint time series and spatial fields of different weather elements APPENDIX 1. SYNOPSIS OF THE THEORY OF STOCHASTIC PROCESSES APPENDIX 2. ON CORRESPONDENCE BETWEEN DISCRETE AND CONTINUOUS LINEAR HOMOGENEOUS STOCHASTIC MODELS APPENDIX 3. CODING OF MULTIPLICATIVE GENERATORS OF PSEUDORANDOM NUMBERS References