Mean square power series solution of random linear differential equations

Abstract

This paper deals with the construction of random power series solutions of linear differential equations containing uncertainty through the diffusion coefficient, the source term as well as the initial condition. Under appropriate hypotheses on the data, we establish that the constructed random power series solution is mean square convergent in a certain interval whose length depends on the mean square norm of the random variable coefficient. Also, the main statistical functions of the approximating stochastic process solution generated by truncation of the exact power series solution are given. Finally, we apply the proposed technique to several illustrative examples.