On solving stochastic initial-value differential equations

This paper addresses the issues involved in solving systems of linear ODE's with stochastic coefficients and loadings described by the Karhunen-Loeve expansion. The Karhunen-Loeve expansion is used to discretize random functions into a denumerable set of uncorrelated random variables, thus providing us for transforming this problem into an equivalent deterministic one. Perturbation error estimates and a priori error estimates between the exact solution and the finite element solution in the framework of Sobolev space are given. The method of successive approximations for finite element solutions is analyzed.