Non-Asymptotic Upper Bounds on the Probability of the epsilon-Atypical Set for Markov Models

For an irreducible, aperiodic finite alphabet Markov chain, consider the set of sequences with atypical probability
Well known results demonstrate that for every is positive, thus the probability of the atypical set decays exponentially fast for sufficiently large values of l. There are many practical situations in which we require good bounds that hold when the parameter is allowed to vary with l in a manner relevant to the problem in question. In this correspondence we derive bounds with this property based on the method of Markov types of Davisson, Longo and Sgarro.

By: Luis Alfonso Lastras-Montaño

Published in: RC22953 in 2003


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