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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