Asymptotic Lower Bounds For Optimal Tracking Problem In Random Environment

This article considers a tracking problem in the random environment,which is modeled by a finite-state,continuous time Markov process.Depending on the structure of cost functions,we establish an asymptotic framework under which the existence of asymptotic lower bounds for this problem is proved.Furthermore,the lower bounds can be explained as a linear programming problem by introducing the occupation measure and the generator of tracking process.