Prykhodko S. The methods of identification of nonlinear stochastic differential systems based on normalizing transformations

The dissertation thesis а new solution of scientific-applied problem of identification of nonlinear stochastic differential systems (SDSs) without the application of brute force method of models, linearization methods and assumptions of normality signals is presented. The methodology for constructing mathematical models of normalized random signals in the form of nonlinear stochastic differential equations (SDEs) is developed. The methodology is based on the application of the normalizing transformations. The method of structural identification of nonlinear SDSs is developed. The method is based on the application of the normalized input and output random signals and normalizing transformations. The modification of generalized method of moments for estimation of confidence intervals of parameters of SDSs is proposed. Mathematical models of extreme sea waves and speech signal in the form of fourth- and eighth-order nonlinear SDEs, nanocarbon particle size distribution in the form of probability density function, random carrier signals in the form of second-order nonlinear SDEs for digital communication system with stochastic process shift keying are constructed.