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- W4380136698 abstract "We prove the large deviation principle for several entropy and cross entropy estimators based on return times and waiting times on shift spaces over finite alphabets. In the case of standard return times, we obtain a nonconvex large-deviation rate function. We consider shift-invariant probability measures satisfying some decoupling conditions which imply no form of mixing nor ergodicity. We establish precise relations between the rate functions of the different estimators, and between these rate functions and the corresponding pressures, one of which is the R'enyi entropy function. The results apply in particular to irreducible Markov chains, equilibrium measures for Bowen-regular potentials, g-measures, invariant Gibbs states for summable interactions in statistical mechanics, and also to probability measures that may be far from Gibbsian, including some hidden Markov models and repeated quantum measurement processes." @default.
- W4380136698 created "2023-06-10" @default.
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- W4380136698 date "2023-06-08" @default.
- W4380136698 modified "2023-09-24" @default.
- W4380136698 title "Large deviations of return times and related entropy estimators on shift spaces" @default.
- W4380136698 doi "https://doi.org/10.48550/arxiv.2306.05277" @default.
- W4380136698 hasPublicationYear "2023" @default.
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