A Canonical Representation for Aggregated Markov Processes

A deterministic function of a Markov process is called an aggregated Markov process. We give necessary and suucient conditions for the equivalence of continuous-time aggregated Markov processes. For both discrete-and continuous-time, we show that any aggregated Markov process which satisses mild regularity conditions can be directly converted to a canonical representation which is unique for each class of equivalent models, and furthermore, is a minimal parameteriza-tion of all that can be identiied about the underlying Markov process. Hidden Markov models on nite state spaces may be framed as aggregated Markov processes by expanding the state space and thus also have canonical representations. 1 Introduction Consider a continuous-time nite state space Markov process, fX(t); t 0g