Mathematical Sciences: Stochastic Processes Applied to Control, Reliability and Replacement

该提案涉及三个主要议题。第一种是利用随机场对圆或圆柱的拟合进行建模。这是必要的，因为涉及这些部件的机器操作的成功取决于比制造过程所能达到的更精细的表面的光滑度。这些空间的随机几何和分析将被研究。第二个主题是复杂设备的可靠性和维护，将在假设组件依赖的情况下进行研究，这将使所得理论更具实用性和适用性。第三个主题将把马尔可夫依赖性的概念扩展到具有无限但呈指数衰减的记忆。

The proposal addresses three major topics. The first one is that of modeling inter fitting circles or cylinders by random fields. This is necessary since the success of the operation of machines involving such components depends on the smoothness of the surfaces that are finer than what can be achieved by the manufacturing processes. The stochastic geometry and analysis of such spaces will be investigated. The second topic of the reliability and maintenance of complex devices will be investigated under the assumed dependence of the components, which will make the resulting theories more practical and applicable. The third topic will extend the idea of markovian dependence to one with infinite but exponentially fading memory.