Numerical Modelling of Random Processes and Fields: Algorithms and Applications
Vasily A. Ogorodnikov, Sergei M. Prigarin · 1996
Part 1 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. Part 2 Spectral models of Gaussian random fields: construction of spectral models spectral models of homogeneous vector fields. Part 3 Numerical models of non-Gaussian processes and fields: consistency conditions of marginal distributions and co-variance 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 disrete processes combined models of non-Gaussian process and fields numerical models of certain classes of non-Gaussian homogeneous processes and fields. Part 4 Convergence of numerical models of random fields in Monte Carlo method: weak convergence of probability measures and random functions conditions of weak convergence in spaces C and Cp 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. Part 5 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. Part 6 Hydrometeorological applications of statistical simulation methods. Appendix: synopsis of the theory of stochastic processes on correspondence between discrete and continuous linear homogeneous stochastic models coding of multiplicative generators of pseudorandom numbers. (Part contents)