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Large deviations for empirical entropies of \(g\)-measures. (English) Zbl 1125.37004

Summary: The entropy of an ergodic finite-alphabet process can be computed from a single typical sample path \(x^n_1\) 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. We prove large deviation principles for conditional, non-conditional and relative \(k(n)\)-block empirical entropies.

MSC:

37A50 Dynamical systems and their relations with probability theory and stochastic processes
37A35 Entropy and other invariants, isomorphism, classification in ergodic theory
37D35 Thermodynamic formalism, variational principles, equilibrium states for dynamical systems
60F10 Large deviations
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