Fedorenko K. The statistical simulation methods of random functions in the problems of environmental monitoring

The work is devoted to investigation of the statistical simulation methods of stationary stochastic processes, homogeneous isotropic random fields on the plane, random fields, which are homogeneous with respect to the time variable and homogeneous isotropic with respect to the spatial variables and if the spectrum is bounded in time variable and their application in the problems of environmental monitoring. The constructed models and developed procedures for statistical simulation of such random are based on the spectral representation of random fields by partial sum of special series and modified Kotelnikov-Shannon decompositions. A model of a Gaussian homogeneous isotropic random field on a plane and the procedure of statistical simulation with Cauchy correlation function with values of the parameters and are built by using the method of spectral coefficients. The method of implementing of statistical simulation of a random field on the plane with Cauchy correlation function by using the method of spectral coefficients is used on the example of studying the chalk deposits strata density at the territory of Rivne NPP and complemented maps of the chalk deposits strata density with additional generated realizations. The method of statistical simulation of stochastic processes and random fields on a plane with a uniform interpolation grid based on modified interpolation Kotelnikov-Shannon decompositions is used in the processing of seismic researches to determine the frequency characteristics of the geological environment under the construction sites. For the first time the theorem of the spectral decomposition of a random field in , which is homogeneous with respect to the time variable and homogeneous isotropic with respect to the spatial variables , is proved. The estimates of the rate of convergence in the mean square of random field by its model are calculated in . For the first time for random fields, which are homogeneous with respect to the time variable and homogeneous isotropic with respect to the spatial variables and if the spectrum is bounded in time variable, the models are constructed in the 4D and dimensional spaces and the statistical simulation procedures, based on the estimates of the rate of convergence in the mean square, of such Gaussian fields are developed with the prescribed accuracy. The developed models and procedures of statistical simulation solve the problems of complementing the monitoring databases without additional observations.