I.N. Sinitsyn, V.I. Sinitsyn, E.R. Korepanov, V.V. Belousov, T.D. Konashenkova, N.N. Semendyaev, I.V. Sergeev, D.A. Basilashvili

The article proceeds the thematic cycle dedicated to software tools for analysis and synthesis of stochastic systems (StS) with high availability for vector random functions and multidimensional linear, quasilinear and nonlinear StS. In section 1 the problem statement is given. Sections 2 and 3 contain main definitions and formulae for canonical expansions (CE) coordinate functions. Statistical estimation and modeling problems in factor analysis are considered in Section 4. Section 5 is devoted to linear transformations based on CE. Quasilinear and nonlinear transformations based on CE are considered in Sections 6 and 7. Appendices 1-5 contains examples of software tools applications.