Mathematical Expectation of the Solution of a Stochastic Multiplicatively Perturbed System of Differential Equations

We consider the Cauchy problem for a first-order linear inhomogeneous system of partial differential equations with random processes as coefficients. Explicit formulas for the mathematical expectation of the solution are obtained. Examples of systems with Gaussian and uniformly distributed random coefficients are considered. An example of calculations for a simplified learning model at the microlevel is given.