Response and Stability of a Random Differential Equation: Part II—Expansion Method

A linear stochastic differential equation of order N with colored noise random coefficients and random input is studied. An approximate expression for the autocorrelation of the response is derived in terms of the statistical properties of the random coefficients and input. This is achieved by using an expansion method known as the Born expansion (Feynman, 1962). Feynman diagrams are used as a short hand notation. In the particular case where the coefficients are white noise processes, the expansion method yields identical results to those obtained using an alternate method in a companion paper (Benaroya and Rehak, 1989). The expansion method is also used to demonstrate that white noise coefficients are statistically uncorrelated from the response.