Zheleznyakova E. The operator representations of stochastic sequences and their applications

The dissertation deals with an operator approach to studying of nonstationary vector stochastic sequences. New characteristics such as an evolutional representativity of vector sequence in Hilbert space, the correlation difference matrix, the vector sequence nonstationarity rank were introduced; those allowed to connect the sequence nonstationarity character with operators' nonunitarity, the latter provide an evolutional representation. The common presentation for correlation difference matrix and for correlation matrix of sufficiently broad range of nonstationar sequences in Hilbert space were obtained with the use of triangular models for contraction.