Simulation of vector random sequences based on polynomial degree canonical decomposition
Vyacheslav S. Shebanin, Igor P. Atamanyuk, Yuriy Panteliyovych Kondratenko · Eastern-European Journal of Enterprise Technologies · 2016
which will make it possible to takefull accountofspecial features of the random sequence under examination, is an important and relevant direction of research. Literature review and problem statementTheoretically accurate methods of simulation of vector random sequences (method of conditional distributions [9] and the Neumann's method [10]) are based on the knowledge of laws of probabilities distribution.At the same time, at present there is no solutionto the problem of tapproximation of multi-dimensional distribution of large dimensionality by statistical data.That is why the existing methods of simulations, which can be realized in technical tools, are developed with essential simplifying assumptions about the properties of random sequences (for example, it is assumed that the examined sequence is scalar, stationary, Markovian, etc.).In particular, for obtaining random sequence with assigned correlation matrix, the method of linear transformations was successfully applied [11].One of the varieties of methods of linear transformations, canonical expansion of V. S. Pugachev [12], makes it possible to form values of the sequence of random variables, dependent within the framework of linear connections with regard to their one-dimensional distribution densities.Furthermore, for the simulation of stationary random sequence,a Fourier series is widely used [13].The apparatus of simulation 4