Mixed Markov Decision Processes in a Semi-Markov Environment with Discounted Criterion

This paper presents a new model: the mixed Markov decision process MDP.in a semi-Markov environment with discounted criterion. It describes a system which behaves like a MDP except that the system is influenced by its semi-Markov process environment. Following each state transition of the environment, the MDP model changes among discrete time MDP, continuous time MDP, and semi-MDP. After presenting the model, we show the validity of the optimality equation and the existence of «-optimal policies. Finally, the mixed MDP in a Markov environment is transformed into a discrete time MDP.