General matrix-valued inhomogeneous linear stochastic differential equations and applications

General extinction results for stochastic partial differential equations and applications

Let L be a positive definite self-adjoint operator on the L2-space associated to a σ-finite measure space. Let H be the dual space of the domain of L1/2 w.r.t. L2(μ). By using an Itô type inequality for the H-norm and an integrability condition for the hyperbound of the semigroup Pt := e −Lt, general extinction results are derived for a class of continuous adapted processes on H. Main applicati...

Stochastic Differential Equations and Applications

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 IR vector-valued inhomogeneous nonlinear stochastic differential equations are reduced to random differential equations, facilitating...

GMRES for oscillatory matrix-valued differential equations

We investigate the use of Krylov subspace methods to solve linear, oscillatory ODEs. When we apply a Krylov subspace method to a properly formulated equation, we retain the asymptotic accuracy of the asymptotic expansion whilst converging to the exact solution. We will demonstrate the effectiveness of this method by computing Error and Mathieu functions. Oxford University Computing Laboratory N...

Stochastic differential equations and integrating factor

The aim of this paper is the analytical solutions the family of rst-order nonlinear stochastic differentialequations. We dene an integrating factor for the large class of special nonlinear stochasticdierential equations. With multiply both sides with the integrating factor, we introduce a deterministicdierential equation. The results showed the accuracy of the present work.

Stochastic Differential Equations with Applications