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Abstract
Let X(0), X(1), X(2),... be a discrete Markov chain with state space S = {1,2,...,m}. Let S be the disjoint union of sets S1, S2, ..., Sr which form a partition of S . De ne Y (n) = i if and only if X(n) ∈ Si for i = 1,2,...,r . Is the Y (n) chain Markov? Such questions come up in learning theory and in other contexts, when the experimenter observes the derived chain Y (n) rather than the original chain X(n). In the homogeneous case, this problem has been studied in details. In this note this problem is studied when the X(n) chain is non-homogeneous and Markov.
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