Mean periodic solutions of a linear inhomogeneous first-order differential equation with random coefficients

Abstract

We obtain deterministic first-order linear differential equations with ordinary and variational derivatives and deterministic initial conditions for the expectation and the second moment function of the solution of an ordinary scalar first-order linear inhomogeneous differential equation whose coefficients are random processes. We derive existence conditions for mean periodic solutions. In particular, we consider Gaussian and uniformly distributed random coefficients.