Statistical behavior of linear systems with randomly varying parameters

Abstract

We consider an nth-order system of ordinary linear differential equations whose coefficients are random functions of the time. In particular, we discuss the case where each of these coefficients is a random noise. A differential equation for the probability distribution of the solutions of the random D. E. is derived and from this the moments can be calculated. Special attention is given to the case of Gaussian noise but the treatment is applicable to any type of noise. Finally, various conditions for stability are discussed.