Abstract:
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.
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