General matrix-valued inhomogeneous linear stochastic differential equations and applications

Abstract

The expressions of solutions for general n × m matrix-valued inhomogeneous linear stochastic differential equations are derived. This generalizes a result of Jaschke [Jaschke, S., 2003. A note on the inhomogeneous linear stochastic differential equation. Insurance: Mathematics and Finance 32, 461–464] for scalar inhomogeneous linear stochastic differential equations. As an application, some R n vector-valued inhomogeneous nonlinear stochastic differential equations are converted to random differential equations, facilitating pathwise study of the solutions.