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In the case of dynamical models that are defined as random walks on a microscopic time-scale, a mesoscopic Markov model should not be confused with the random walk microscopic dynamics. Even for such a dynamical system, we can ask whether a mesoscopic Markov model exists for any particular value of τmes. Moreover, Markov behavior on the mesoscopic time-scale for mesostates is not a trivial consequence of random walk microscopic dynamics.
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