On the numerical integration of the undamped harmonic oscillator driven by independent additive gaussian white noises

Abstract

The stochastic exponential method is applied to solve the undamped linear stochastic oscillator driven by a multidimensional Wiener process. The proposed additive noise model is new since the disturbances are introduced in the equivalent first order two dimensional system and can affect both space and velocity. It is shown that three important properties related to long time behavior of its analytical solution are preserved. In addition, the mean-square error of the numerical solution is analyzed. Numerical experiments confirming the theoretical results are presented.