AUTOMATED 1ST AND 2ND-ORDER MOMENT EQUATIONS FOR A SET OF STOCHASTIC DIFFERENTIAL-EQUATIONS OF TYPE AZ+BZ=C(T)

The generation of the second and higher order moment equations for a s et of stochastic differential equations based on Ito's differential le mma is difficult, even for small system of equations. From the knowled ge of the statistical properties of the Gaussian white noises associat ed with the parameters and input coefficients of a set of stochastic d ifferential equations of type A.Z+B.Z = C(t), a way to automatically g enerate the second order moment equations in a computer is presented i n this paper. The resulting set of first and second order moment equat ions is also presented in the same state-space form of the original se t of stochastic differential equations through a vectorization of the correlation matrix, which takes advantage of its symmetry. The procedu re involved here avoids the inversion of matrix A to apply Ito's diffe rential lemma. Therefore, the presented numerical implementation reduc es the computational effort required in the formulation and solution o f the moment equations. Moreover, other robust and efficient numerical deterministic integration schemes can be equally applied to the solut ion of the moment equations.