Abstract.
We prove an exponential inequality for the absolutely continuous invariant measure of a piecewise expanding map of the interval. As an immediate corollary we obtain a concentration inequality. We apply these results to the estimation of the rate of convergence of the empirical measure in various metrics and also to the efficiency of the shadowing by sets of positive measure.
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Received: 14 August 2001 / Revised version: 13 February 2002 / Published online: 1 July 2002
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Collet, P., Martinez, S. & Schmitt, B. Exponential inequalities for dynamical measures of expanding maps of the interval. Probab Theory Relat Fields 123, 301–322 (2002). https://doi.org/10.1007/s004400200204
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DOI: https://doi.org/10.1007/s004400200204
Keywords
- Invariant Measure
- Positive Measure
- Dynamical Measure
- Empirical Measure
- Concentration Inequality