ASPECTS SIMULATION OF VECTOR RANDOM SEQUENCES BASED ON POLYNOMIAL DEGREE CANONICAL

synthesis of the models of chemical kinetics, technological and economic processes control [7], etc. The existence of preliminary stage of accumulation of information about the objectunder examination is a character-istic peculiarity of these problems. The probabilistic nature of external influence and of the coordinates (input, output) of the RCCF objects under conditions of sufficient amount of statistical data determines the need and expediency of applying deductive [8] methods of simulation of random sequences for their solution. The possibility of accumulation of statistical data makes it possible to quite accurately determine characteristics of random sequences. That is why improvement of those existing and development of the new methods of


Introduction
A special feature of a wide circle of applied problems in different areas of science and technology is the probabilistic nature of the studied phenomenon or existence of influence on the object from random factors, as a result of which the process of changing its state also acquires the probabilistic nature. The objects of such a class, which relate to the objects with randomly changing conditions of functioning (RCCF), are examined, for example, when solving the problems of technical [1] and medical diagnostics [2], radio engineering [3], automation [4], predicting control of reliability [5], information protection [6], synthesis of the models of chemical kinetics, technological and economic processes control [7], etc.
The existence of preliminary stage of accumulation of information about the objectunder examination is a characteristic peculiarity of these problems. The probabilistic nature of external influence and of the coordinates (input, output) of the RCCF objects under conditions of sufficient amount of statistical data determines the need and expediency of applying deductive [8] methods of simulation of random sequences for their solution.
The possibility of accumulation of statistical data makes it possible to quite accurately determine characteristics of random sequences. That is why improvement of those existing and development of the new methods of simulations,

SIMULATION OF VECTOR RANDOM SEQUENCES BASED ON POLYNOMIAL DEGREE CANONICAL DECOMPOSITION V . S h e b a n i n
Doctor of Technical Sciences, Professor, Rector* I . A t a m a n y u k of stationary normal sequences is also rather well examined on the basis of two operators of generation of values, proposed in [14], as well as the developed [15] approaches to determining their parameters. In this case, the problem of simulation of Markovian sequences is solved most easily [16], which comes down to implementation of the method of conditional distributions for the simplest case -only with the two-dimensional distribution density. However, the introduction of simplifying assumptions about the properties of random sequence substantially limits the accuracy of solution of the problems of simulation of random sequences in the RCCF objects necessary for practical applications. That is whyit isundoubtedly a rather promising problem to develop efficient method of modellinga vector random sequence, which would set no substantial limitations on the properties of the examined random sequence.

Aims and objectives of the study
The purpose of the work is to increase accuracy of simulation of vector random sequence by a fulleruse of information about its stochastic properties.
To achieve the goal, the following tasks were to be solved: -synthesis of mathematical model of vector random sequence taking full account of stochastic parameters; -developmentof a method for generating realizations of vector random sequences based on the obtained mathematical model; -verifying effectiveness of the proposed method of simulation with the aid of numerical experiment on PC.

Mathematical model and method forgenerating realizations of vector random sequences
Let us assume that vector random sequence { } ( ) = h X X i , = i 1,I, = h 1,H in the examined row of points i t , = i 1,I is fully determined by the discretized moment functions The elements of canonical representation (1) are determined by formulas: Realizations of vector random sequence are obtained by conversion by expression (1) of H arrays of values of random coefficients Random sequence Simulation of vector random sequence with the use of expression (6) starts from generation of value (1)   11 w with the required distribution density, whose estimation is preliminarily obtained based on statistical information about the examined sequence. Using ( x 1 M X 1 w (1) M X 1 w .
Then coefficients (2) (3) (N) 11 11 11 w ,w ,...,w are determined consecutively for the first component with the aid of ratio  (1)  with the required distribution law, the value x 1 (2) of the first component of the simulated vector random sequence is formed: The block diagram, which reflects special features of computational process of the formation of realizations of vector random sequence according to model (6), as wellas overall scheme of generating realizations, are represented in Fig. 1, 2.
The main stages of the method for generating realizations of vector random sequences based on model (6) are: -accumulation of realizations of random sequence; -calculation of discretized moment functions based on statistical information; -formation of canonical decomposition (6) with the use of moment functions; -estimation of distribution densities of the coefficients of canonical decomposition; -generation of values of random coefficients with the required distribution laws with their subsequent conversion with the aid of expression (7).
If stochastic connections between the components are absent

Discussion of results of the numerical experiment
The method for generating realizations of vector sequence based on decomposition (6) is verified for the vector model ( ) ( ) ( ) ( ) ( ) where X 1 (1)  Results of preliminary analysis of estimations of moment functionsrevealed that for this sequence, the connections of the order of nonlinearity ≤ N 4. are the significant stochastic connections.
Using expression (7) based on statistical sample of 500 realizations of sequence (14), (15), for N=4 we obtained histograms of frequencies of n random coefficients  The procedure of obtaining realizations of vector random sequence (14), (15) on the basis of canonical decomposition (6) comes down to the generation of values of the random variables (1) (1) i1 i2 W , W , = i 1,7 with the appropriate assigned laws of distribution (Fig. 3-16) and to the conversion of the obtained values by expression (6).   (1), by the polynomial scalar (10) and vector decomposition (6) Analysis of the resultsdemonstrated in Fig. 17 indicates low accuracy of the representation of the examined model (14), (15) with the help of linear canonical decomposition (1). In this case, a relative error of approximation of the first component ( ) 1 X i , = i 1,7 in the points of discretization ≥ i 5 is equal to 8,1-8,5 %. Fig. 17 also illustrates obtaining essential additional gain (2,0-2,5 %) in accuracy of the representationof random sequence with the aid ofpolynomial vector decomposition (6) in comparison with the polynomial scalar decomposition (10) due to the use of stochastic connections between the components.

Conclusions
As a result of conducted research,we obtained a polynomial canonical decomposition of vector random sequence, which, in contrast to the known canonical model, takes full account of nonlinear stochastic connections.
Based on the synthesized mathematical model, we developed a method for generating realizations of vector random sequenceswith the required characteristics. Vector canonical decomposition and the method for generating realizations set no any substantial constraints on the class of the examined random sequences (linearity, Markovian behavior, stationarity, monotony, etc.). Taking into account the recurrent nature of determiningthe elements of vector canonical representation, the procedure of simulation of random sequences proves to be sufficiently simple in computational sense.
Results of the numerical experiment demonstrated high accuracy of simulation of vector sequence with the aid of the developed method.
The method may be applied in different areas of science and technology, connected to examining the objects whose parameters are of stochastic nature.

Introduction
The process of managing a modern organization is characterized by a high degree of uncertainty of the external and internal environment, which entails the need to make informed management decisions based on all sorts of risks. This necessitates the need to facilitate management by using some modern information technology [1] and a decision support system (DSS). Despite the continuous growth of the accompanying organizational information management [2], a significant number of problems in management decisions can be reduced to the classical models of game theory, for example, to the problem of choosing the optimal pure strategy in conditions of complete uncertainty. This task does not imply a unique solution by virtue of the main limitations, namely the total uncertainty of the external environment. Such circumstances most clearly reveal the problem of choosing a criterion to determine the best strategy. In the case of multiple expert assessments (individual or group) of the effectiveness of managerial decisions, it is important to choose not only a particular criterion but also the tools of its parameter setting for a particular problem to be solved. It determines the relevance of developing mathematical models to compare alternatives that analytically include factors