Mathematical Sciences: Topics in Stochastic Control and Diffusion Processes

在随机控制问题中，观察到一种随机现象， 是要控制使用知识的概率法则， 现象服从和观察的过去历史。 目标是 以最小化相关成本函数的期望值。 虽然动态propramming原则将在理论上产生一个 最优策略，在实践中，理论结果很少提供 明确可计算的答案。 其中一个主要的目标是 研究的目的是尽可能明确地确定 在特定的随机控制问题中的最优策略， 消费/投资问题。 其他研究将涉及 最优停止问题与奇异随机问题之间的联系 控制 后者涉及具有奇异部分的控制动作。 特别感兴趣的是所谓的“有限燃料”约束，其中 控制器可用的努力（燃料）量是有限的。

In stochastic control problems, a random phenomenon is observed which is to be controlled using knowledge of the probabalistic law that the phenomenon obeys and the past history of the observations. The goal is to minimize the expected value of an associated cost function. Although the dynamic propramming principle will in theory yield an optimal strategy, in practice the theoretical results rarely provide explicitly computable answers. One of the main objects of this research is to determine, as explicitly as possible, the form of optimal policies in specific stochastic control problems arising from consumption/investment issues. Other research will deal with the connections between optimal stopping problems and singular stochastic control. The latter involves control actions having singular parts. Of particular interest are so-called 'finite fuel' constraints wherein the amount of effort (fuel) available to the controller is limited.