Closure method and asymptotic expansions for linear stochastic systems |
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| Authors: | Roman V Bobryk |
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| Institution: | a Institute of Mathematics, Swietokrzyska Academy, 25406 Kielce, Poland
b Institute APMM, National Academy of Sciences, 79060 Lviv, Ukraine |
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| Abstract: | A closure procedure for the hierarchy of moment equations related to linear systems of ordinary differential equations with a random parametric excitation is introduced. A generalization of Pringsheim's theorem for continued fractions is used in a proof of the procedure convergence. The boundary function method for singular perturbation problems is applied to obtain asymptotic expansions for the moments of the solutions of such systems. |
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| Keywords: | Linear stochastic system Moments Matrix continued fraction Singular perturbation |
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