Extended a Class of Singular Stochastic Control Models of "Fail-Stop"

This paper extends a class of discount problem of singular stochastic control with stopping time. We extend the state process and cost function to general case. By stochastic analysis and optimal control theory, the "fail-stop" control strategy is its optimal control. The conditions of the "fail-stop" strategy and optimal control function and control method are given. The conclusion in this paper has a fairly deep application.