Lp-SOLUTIONS OF BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS

Reflected Solutions of Backward Doubly Stochastic Differential Equations ∗

We study reflected solutions of one-dimensional backward doubly stochastic differential equations (BDSDEs in short). The “reflected” keeps the solution above a given stochastic process. We get the uniqueness and existence by penalization. For the existence of backward stochastic integral, our proof is different from [KKPPQ] slightly. We also obtain a comparison theorem for reflected BDSDEs. At ...

On Solving Backward Doubly Stochastic Differential Equations

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...

Pathwise Stationary Solutions of Stochastic Partial Differential Equations and Backward Doubly Stochastic Differential Equations on Infinite Horizon

The main purpose of this paper is to study the existence of stationary solution for stochastic partial differential equations. We establish a new connection between backward doubly stochastic differential equations on infinite time horizon and the stationary solution of the SPDEs. For this we study the existence of the solution of the associated BDSDEs on infinite time horizon and prove it is a...

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/...