Moments of solutions of evolution equations and suboptimal programmed controls

Moments of solutions of non-linear differential equations subjected to random perturbations satisfy infinite systems of equations that do not contain finite closed subsystems. One of the methods for approximate solution of such infinite systems consists in replacing them by finite systems obtained from the original one as a result of equating to zero all the moments of sufficiently high order. It is shown that the moments of solutions of a wide class of ordinary differential equations, as well as of certain classes of partial differential equations, are approximated by solutions of those finite systems. The results obtained are used for constructing suboptimal programmed controls of dynamical systems with random parameters. Bibliography: 10 titles.