Chazottes, J.-R.; Gabrielli, D. Large deviations for empirical entropies of \(g\)-measures. (English) Zbl 1125.37004 Nonlinearity 18, No. 6, 2545-2563 (2005). 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. Cited in 7 Documents 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 Keywords:entropy-estimation problem PDFBibTeX XMLCite \textit{J. R. Chazottes} and \textit{D. Gabrielli}, Nonlinearity 18, No. 6, 2545--2563 (2005; Zbl 1125.37004) Full Text: DOI arXiv