Solving linear and quadratic random matrix differential equations using: A mean square approach. The non-autonomous case

This paper is aimed to extend, the non-autonomous case, the results recently given in the paper Casabán et al. (2016) for solving autonomous linear and quadratic random matrix differential equations. With this goal, important deterministic results like the Abel-Liouville-Jacobi's formula, are extended to the random scenario using the so-called Lp-random matrix calculus. In a first step, random time-dependent matrix linear differential equations are studied and, in a second step, random non-autonomous Riccati matrix differential equations are solved using the hamiltonian approach based on dealing with the extended underlying linear system. Illustrative numerical examples are also included.