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Information × Registration Number 0217U007476, 0115U000087 , R & D reports Title Analytical methods of stochastic differential equations popup.stage_title Head Baiev Artem Victorovich, Registration Date 15-01-2018 Organization Donetsk State University popup.description2 Object of study. Gaussian random processes and fields. Subject of study. Correlation functions of stochastic processes and fields, norms of quadratic-Gaussian random processes, Gaussian random field models, Gaussian stationary processes with stable correlation function, behavior and properties of these processes. The aim of the study. Find estimates for the correlation functions of stochastic processes and fields, assess the norms of quadratic-Gaussian random processes, find a method for constructing models of Gaussian random fields in different functional spaces. Find estimates for the distribution of supremum of Gaussian stationary processes with a stable correlation function, to study the behavior of these processes at infinity, to investigate some analytic properties of these processes. Research methods. Probabilistic methods, methods of modeling. Main results of work. The stationary own complex random processes, stationary own complex random processes with stable correlation function are investigated. Some results for the properties of a stable correlation function are presented in [11]. We introduced some properties of quadratic Gaussian random variables and processes (see, for example, [3, 7, 8]). Also, in this paper we obtain estimates of the distributions of the functionals of the module of stationary Gaussian intrinsic complex random processes (see, for example, [13, 6, 10]). Theorems describing the behavior of the module of a stationary intrinsic complex random process at infinity are developed. The space of sub-Gaussian random variables Sub (?), Orlich space of random variables L_U (?) and space of quadratic-Gaussian random variables are considered. The problem of estimating exponential moments of quadratic forms from random variables from the space SG_? (?) and the boundaries in the quadratic quadratic forms of such quadratic forms is considered. Models of Gaussian non-stationary random processes with given precision and reliability are constructed. The conditions for selecting a partition of a set are studied so that the constructed model approximates a Gaussian non-stationary random process with given reliability and accuracy in the spaces C (T) and L_p (T). RANDOM PROCESSES, PROCESS SPCR, GAUSSIAN RANDOM PROCESSES, MODELING, ACCURACY AND RELIABILITY MODELING, SUBHAUSSOVI RANDOM VARIABLES DISTRIBUTION ASSESSMENT Product Description popup.authors Баев Артем Викторович Болдирєва Валерія Олегівна Козаченко Юрій Васильович Козир Сергій Михайлович Петранова Марина Юріївна popup.nrat_date 2020-04-02 Close