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Registration Number

0215U004970, 0111U006680 , R & D reports

Title

Problems of decision making theory and stochastic networks system analysis

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Head

Nakonechny Olexandr Grygorovych,

Registration Date

23-12-2015

Organization

National Taras Shevchenko University of Kiev

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Object of study: the problems of minimax estimation and optimal control, the basic structure of the matrix Euclidean spaces, queuing systems, shot noise processes, random walks with a barrier, balleans. Objective: To investigate some problems of decision making theory and system analysis under uncertainty and conflict. To investigate the system analysis problems for controlled stochastic systems of network structure. To investigate some random and deterministic discrete combinatorial structures. Methods of research: Methods of decision making theory, minimax estimation, optimal control theory, theory of stochastic systems and networks, mathematical statistics and data analysis, renewal theory, combinatorial optimization methods on groups. Numerical algorithms for guaranteed estimation of boundary value problems for elliptic equations under uncertainty are developed. An algorithm for constructing an approximate optimal control for Poisson equation with nonlocal boundary conditions is developed. A multilevel structure for smoothing affine invariant classifier of extrapolation depth is proposed. Constructive tools to operate in matrix Euclidean spaces are offered. Explicit formulae are obtained for stationary probabilities of Markov chain that describes the operation of the system with retrial queues and controlled properties. We developed an algorithm for solving the optimization problem for such a system and algorithm for evaluating nonstationary parameters vector under nonclassical assumptions at real time. For non-Gaussian random processes the estimates of probabilities of certain events were found. A module was created to test problems of arbitrary types. We proved limit theorems for finite-dimensional distributions of shot noise processes with non-increasing response functions and for random. The characteristic of balleans accurate to rough equivalence was given, cellularity criteria was obtained, basic cardinal invariants of balleans were calculated. For problems of optimal bilateral choice Nash equilibrium situation was found in the form of threshold strategies of agents.5481

Product Description

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Іксанов Олександр Маратович
Галкін Олександр Анатолійович
Демченко Ірина Юріївна
Доценко Сергій Іванович
Зінько Тарас Петрович
Какойченко Андрій Ігоревич
Капустян Олена Анатоліївна
Коробко Тетяна Вікторівна
Кучеренко Oльга Василівна
Лебєдєв Євген Олександрович
Лосєва Марія Вікторівна
Лукович Oльга Василівна
Нікітін Анатолій Володимирович
Пашко Анатолій Олексійович
Подлипенко Юрій Костянтинович
Пономарьов Вадим Дмитрович
Протасов Ігор Володимирович
Усар Ірина Ярославівна

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2020-04-02