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The behavior of an informationally closed and generative system that is specified by transition probabilities (see probability) between that system's states. It is named after A. A. Markov who at the turn of the century studied poetry and other texts as stochastic sequences of characters (symbols, letters, syllables, and words). The probabilities of a Markov chain are usually entered into a transition matrix indicating which state or symbol follows which other state or symbol. The order (see ordinality) of a Markov chain corresponds to the number of states or symbols from which probabilities are defined to a successor. Ordinarily, Markov chains are state determined or of the first order. Higher orders are history determined. An unequal distribution of transition probabilities is a mark of a Markov chain's redundancy and a prerequisite of predictability (see information theory). (Krippendorff)
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