Large deviations for empirical entropies of Gibbsian sources

Details Large deviations for empirical entropies of Gibbsian sources Large deviations for empirical entropies of Gibbsian sources

2004-06-04

arxiv.org/abs/math/0406083v3

Mathematics

Probability

19 pages; revised version; to appear in Nonlinearity

Scientific paper

10.1088/0951-7715/18/6/007

The entropy of an ergodic finite-alphabet process can be computed from a single typical sample path x_1^n using the entropy of the k-block empirical probability and letting k grow with $n$ roughly like log n. We further assume that the distribution of the process is a g-measure; g-measures form a large class of Gibbs measures. We prove large deviation principles for conditional, non-conditional and relative k(n)-block empirical entropies.

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