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

Abstract

[EN] This paper is aimed to extend, the non-autonomous case, the results recently given in the paper [1] 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 $\mathrm{L}_{p}$-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. [1] M.-C. Casabán, J.-C. Cortés, L. Jódar, Solving linear and quadratic random matrix differential equations: A mean square approach, Applied Mathematical Modelling 40 (2016) 9362-9377.