Moment functions for a solution of a stochastic system of partial differential equations

In this paper, we consider the Cauchy problem for a linear inhomogeneous system of first-order partial differential equations with two random coefficients and a random inhomogeneity. Explicit formulas for the moment functions of the solution are obtained: mathematical expectation, mixed moment functions, and the second moment function. As applications, explicit formulas for mixed moment functions and the second moment function for solutions of an equation with independent Gaussian random coefficients are obtained.