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- W2101123485 abstract "Motivated by entropy estimation from chaotic time series, we provide a comprehensive analysis of hitting times of cylinder sets in the setting of Gibbsian sources. We prove two strong approximation results from which we easily deduce pointwise convergence to entropy, lognormal fluctuations, precise deviation estimates and an explicit formula for the hitting-time multifractal spectrum. It follows from our analysis that the hitting time of a $n$-cylinder fluctuates in the same way as the inverse measure of this $n$-cylinder at small scales, but in a different way at large scales. In particular, the Renyi entropy differs from the hitting-time spectrum, contradicting a naive ansatz. This phenomenon was recently numerically observed for return times that are more difficult to handle theoretically. The results we obtain for return times, though less complete, improve the available ones." @default.
- W2101123485 created "2016-06-24" @default.
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- W2101123485 date "2004-11-12" @default.
- W2101123485 modified "2023-09-25" @default.
- W2101123485 title "Entropy estimation and fluctuations of Hitting and Recurrence Times for Gibbsian sources" @default.
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