Backward Stochastic Differential Equation and Exact Controllability of Stochastic Control Systems

<正> This paper is concerned with the structures of the backward stochastic differentialequations (BSDE). We provide an approach to the determination of whether aformulation of certain types of BSDE is well-posed in the existenee viewpoint. As anapplication of our results, we give a necessary condition of tenrminal controllability fora stochastic control system. To linear stochastic control systems, we introduce a purealgebraic criterion of necessary and sufficient condition for a system to be exactlycontrollable.