A numerical scheme for backward doubly stochastic differential equations

Numerical scheme for backward doubly stochastic differential equations

We study a discrete-time approximation for solutions of systems of decoupled forward-backward doubly stochastic differential equations (FBDSDEs). Assuming that the coefficients are Lipschitz-continuous, we prove the convergence of the scheme when the step of time discretization, |π| goes to zero. The rate of convergence is exactly equal to |π|1/2. The proof is based on a generalization of a rem...

On Solving Backward Doubly Stochastic Differential Equations

Numerical Method for Backward Stochastic Differential Equations

We propose a method for numerical approximation of Backward Stochastic Differential Equations. Our method allows the final condition of the equation to be quite general and simple to implement. It relies on an approximation of Brownian Motion by simple random walk.

Numerical Solutions for Forward Backward Doubly Stochastic Differential Equations and Zakai Equations

NUMERICAL SOLUTIONS FOR FORWARD BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS AND ZAKAI EQUATIONS Feng Bao, Yanzhao Cao, & Weidong Zhao Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849 School of Mathematics, Sun Yat Sun University, China School of Mathematics, Shangdong University, Jinan, China Original Manuscript Submitted: 05/22/2011; Final Draft Received: 08/...

Stochastic PDEs and Infinite Horizon Backward Doubly Stochastic Differential Equations

We give a sufficient condition on the coefficients of a class of infinite horizon BDSDEs, under which the infinite horizon BDSDEs have a unique solution for any given square integrable terminal values. We also show continuous dependence theorem and convergence theorem for this kind of equations. A probabilistic interpretation for solutions to a class of stochastic partial differential equations...