General Matrix-Valued Inhomogeneous Linear Stochastic Differential Equations and Applications

Abstract

The expressions of solutions for general $n\times m$ matrix-valued inhomogeneous linear stochastic differential equations are derived. This generalizes a result of Jaschke (2003) for scalar inhomogeneous linear stochastic differential equations. As an application, some ${\mathbb{R}}^n$ vector-valued inhomogeneous nonlinear stochastic differential equations are reduced to random differential equations, facilitating pathwise study of the solutions.