Anticipated backward doubly stochastic differential equations

Anticipated Backward Stochastic Differential Equations

In this paper, we discuss a new type of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present but also the future. We show that these anticipated BSDEs have unique solutions, a comparison theorem for their solutions, and a duality between them and ...

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...

Anticipated Backward Stochastic Differential Equations with Continuous Coefficients

In this paper we prove the existence of solutions to 1-dimensional anticipated backward stochastic differential equations with continuous coefficients. We also establish the existence of a minimal solution. Finally we derive a related comparison theorem for these minimal solutions.

Some properties of generalized anticipated backward stochastic differential equations ∗

In this paper, after recalling the definition of generalized anticipated backward stochastic differential equations (generalized anticipated BSDEs for short) and the existence and uniqueness theorem for their solutions, we show there is a duality between them and stochastic differential delay equations. We then provide a continuous dependence property for their solutions with respect to the par...