Large deviations and the rate of convergence in the Birkhoff ergodic theorem |
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| Authors: | A. G. Kachurovskii I. V. Podvigin |
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| Affiliation: | 1. Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk, Russia
2. Novosibirsk State University, Novosibirsk, Russia
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| Abstract: | For bounded averaged functions, we prove the equivalence of the power-law and exponential rates of convergence in the Birkhoff individual ergodic theorem with the same asymptotics of the probability of large deviations in this theorem. |
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