Closure method and asymptotic expansions for linear stochastic systems

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. © 2006 Elsevier Inc. All rights reserved.