MATH 3989 Mathematics Project NON - ASYMPTOTIC EQUIPARTITION PROPERTIES FOR HIDDEN MARKOV PROCESSES
نویسندگان
چکیده
A hidden Markov process (HMP) is a discrete-time finite-state homogeneous Markov chain observed through a discrete-time memoryless invariant channel. The non-asymptotic equipartition property (NEP) is a bound on the probability of the sample entropy deviating from the entropy rate of a stochastic process, so it can be viewed as a refinement of Shannon-McMillan-Breiman theorem. In this report, we start from the basic concept and properties of a hidden Markov process, the introduction of the Rényi entropy rate and a review of Shannon-McMillan-Breiman theorem. Then we will study a NEP for independent and identically distributed sources, a NEP for hidden Markov processes and a conjectured stronger NEP for hidden Markov processes which relates the Rényi entropy rate surprisingly. Finally, we conclude with possible future works on this subject.
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