We investigate a functional limit theorem (homogenization) for Reflected Stochastic Differential Equations on a half-plane with stationary coefficients when it is necessary to analyze both the effective Brownian motion and the effective local time. We prove that the limiting process is a reflected non-standard Brownian motion. Beyond the result, this problem is known as a prototype of non-trans...

For system identification, the ordinary differential equations (ODEs) model is popular for its accuracy and effectiveness. Consequently, the ODEs model is extended to the stochastic differential equations (SDEs) model to tackle the stochastic case intuitively. But the existence of stochastic integral is a rigid barrier. We simply transform the SDEs to their corresponding stochastic difference e...

In this article, we summarize some results on the existence and qualitative behavior of stochastic dynamical systems in infinite dimensions. The three main examples covered are stochastic systems with finite memory (stochastic functional differential equations-sfde’s), semilinear stochastic evolution equations (see’s) and stochastic partial differential equations (spde’s). Due to limitations of...

The paper consists of two parts. In the first part of the paper, we proposed a procedure to estimate local errors of low order methods applied to solve initial value problems in ordinary differential equations (ODEs) and index-1 differential-algebraic equations (DAEs). Based on the idea of Defect Correction we developed local error estimates for the case when the problem data is only moderately...

This paper is intended to give a probabilistic representation for stochastic viscosity solution of semi-linear reflected stochastic partial differential equations with nonlinear Neumann boundary condition. We use its connection with reflected generalized backward doubly stochastic differential equations. AMS Subject Classification: 60H15; 60H20

This paper considers the backward error analysis of stochastic differential equations (SDEs), a technique that has been of great success in interpreting numerical methods for ODEs. It is possible to fit an ODE (the so called modified equation) to a numerical method to very high order accuracy. Backward error analysis has been particularly valuable for Hamiltonian systems, where symplectic numer...

in this paper, we present an efficient method for determining the solution of the stochastic second kind volterra integral equations (svie) by using the taylor expansion method. this method transforms the svie to a linear stochastic ordinary differential equation which needs specified boundary conditions. for determining boundary conditions, we use the integration technique. this technique give...

In this paper, we study the recursive stochastic optimal control problems. The control domain does not need to be convex, and the generator of the backward stochastic differential equation can contain z. We obtain the variational equations for backward stochastic differential equations, and then obtain the maximum principle which solves completely Peng’s open problem.

This paper is intended to give a probabilistic representation for stochastic viscosity solution of semi-linear reflected stochastic partial differential equations with nonlinear Neumann boundary condition. We use its connection with reflected generalized backward doubly stochastic differential equations. AMS Subject Classification: 60H15; 60H20