The evolution of aggregated Markov chains

For a stationary two-sided Markov chain with finite state-space I and a partition we consider the aggregated sequence defined by Yn=[nu] if Xn[set membership, variant]I[nu], which is also stationary but in general not Markovian. We present a tractable way to determine the transition probabilities of , either given a finite part of its past or given its infinite past. These probabilities are linked to the Radon-Nikodym derivative of PUnXn=i with respect to PUn, where .

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