Approximate dimension reduction for filtered Markov chains

This paper presents an efficient and applicable approximate dimension reduction method for the optimal filter of a partially observable system in which both the state and observation processes are jump processes. After classifying the states of state and joint processes into fast and slow states based on the structures of their transition rate matrices, the reduced dimension filter is obtained by deleting the fast states from the system and properly modifying the transition rates among the slow states. The paper also present an error analysis and an example of numerical simulation for the method.