General Matrix-Valued Inhomogeneous Linear Stochastic Differential Equations and Applications

2008/08/07 by Jinqiao Duan, Duan, Jinqiao, Jia-an Yan +2 · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Theoretical and Computational Physics #math.DS #math.PR

paper · pdf · doi:10.48550/arxiv.0808.1112

arxiv created 2008/08/07 · openalex publication_date 2008/08/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

The expressions of solutions for general n× 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 \Rⁿ vector-valued inhomogeneous nonlinear stochastic differential equations are reduced to random differential equations, facilitating pathwise study of the solutions.

Citations

• Random dynamical systems

Cited by

• Physical Reduced Stochastic Equations for Continuously Monitored Non-Markovian Quantum Systems with a Markovian Embedding

Related

• Matrix-valued SDEs arising from currency exchange markets
• Stochastic differential equations related to random matrix theory
• Some Distributional Properties of Linear Stochastic Differential Equations
• A Complete Decomposition of Stochastic Differential Equations
• Harmonic Analysis of Stochastic Equations and Backward Stochastic Differential Equations