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

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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.