Numerical Modelling of Random Processes and Fields

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