The principal investigators will study stochastic process models for systems which are naturally monotone and they will solve stochastic control problems for these systems. One important application for such processes is in optimal control and replacement problems for systems subject to deterioration and failure. They will work with a class of system models for wear in which one component of a vector process is monotone. These systems are constructed from diffusions and dynamic programming techniques for the analysis of controlled diffusions can be extended. The monotonicity of the wear process provides additional structure and their analysis will take advantage of this structure. The principal investigators will study stochastic process models for systems which are naturally monotone and they will solve stochastic control problems for these systems. One important application for such processes is in optimal control and replacement problems for systems subject to deterioration and failure. This area of application combines tools from the areas of probability and applied mathematics.
