Pashko A. Simulation of random processes and fields with accuracy and reliability

The dissertation is devoted to the research of sub-Gaussian models for statistical modeling of random processes and fields. The scientific bases of sub-Gaussian models for statistical modeling of random processes and fields with the specified accuracy and reliability were constructed. Main lines of investigation - convergence research and obtaining accuracy and reliability estimates of sub-Gaussian models for spectral representations of random processes and fields in the form of random series, convergence research and obtaining accuracy and reliability estimates of sub-Gaussian models for spectral representations of random processes and fields depicted in the form of stochastic integrals. In particular, investigated Karhunen -Loeve images, Fourier images, and processes with discrete spectrum in different functional spaces. Conditions and rate of convergence estimation are obtained for sub-Gaussian models of random processes and fields in the spaces Lp, Orlicz spaces and continuous functions spaces. Based on the results we built computational algorithms for statistical modeling of random processes and fields with given precision and reliability. Particular attention was paid to computational algorithms and statistical modeling Wiener and generalized Wiener processes. Further research step of properties of sub-Gaussian and strictly sub-Gaussian random variables, processes and fields was developed.