Some Issues About The (Forward) Backward Stachastic Differicial Equation

In this paper, we prove the existence and the uniqueness of the infinite horizon FBSDE in and obtain the scope of k. Under the conclusion of this, we prove the exponential asymptotical stability of the solution. We also obtain the existence and uniqueness ofaDuffie-Epstein BSDE with non- Lipschitz coefficients. Moreover, we consider a specialmodel of FBSDE , Stochastic Hamiltonian equation. Here we solved the stochastic Hamiltonian equation with boundary conditions of non-zero. Further more, we find the solution of it, and point out that the eigenfunctions has the phenomenon of stochastic vibrations and the related statistic periodicity.