Wide sense one-dependent processes with embedded Harris chains and their applications in inventory management

In this paper we consider stochastic processes with an embedded Harris chain. The embedded Harris chain describes the dependence structure of the stochastic process. That is, all the relevant information of the past is contained in the state of the embedded Harris chain. For these processes we proved a powerful reward theorem. Futher, we show how we can control these type of processes and give a formulation similar to semi-Markov decision processes. Finally we discuss a number of applications in inventory management.