Infinite horizon backward stochastic differential equation and exponential convergence index assignment of stochastic control systems

This paper studies exponential convergence index assignment of stochastic control systems from the viewpoint of backward stochastic di'erential equation. Like deterministic control systems, it is shown that the exact controllability of an open-loop stochastic system is equivalent to the possibility of assigning an arbitrary exponential convergence index to the solution of the closed-loop stochastic system, formed by means of suitable linear feedback of the states. As an application, a su7cient and necessary condition for the existence and uniqueness of the solution of a class of in!nite horizon forward–backward stochastic di'erential equations is provided. ? 2002 Elsevier Science Ltd. All rights reserved.