Atamanyuk I. The mathematical models of the processes in the objects with randomly variable conditions of functioning and the methods of their state prognosis.

The thesis is devoted to the solving of important scientific and technical problem of the formation of the complex of mathematical models and methods of generation, recognition and prognosis of the state of the objects with randomly variable conditions of the functioning on the basis of the canonical expansions with taking into account the randomness of the degree of nonlinear relations and the number of the dots of the discretization of the random sequences of the coordinates of objects. The methods of the generation, recognition and extrapolation of the realizations of scalar and vector random sequences on the basis of polynomial degree and extended nonlinear canonical expansions are developed. Nonlinear stochastic relations between two random dots of discretezation are taken into account in polynomial degree model. All possible information about random sequence including multiple nonlinear stochastic relations of random dimension is used in extended nonlinear model. The mathematical models and methods obtained during work don't impose any limitations on the class of random sequences which are investigated.