Electronic Communications in Probability

Growth of normalizing sequences in limit theorems for conservative maps

Sébastien Gouëzel

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We consider normalizing sequences that can give rise to nondegenerate limit theorems for Birkhoff sums under the iteration of a conservative map. Most classical limit theorems involve normalizing sequences that are polynomial, possibly with an additional slowly varying factor. We show that, in general, there can be no nondegenerate limit theorem with a normalizing sequence that grows exponentially, but that there are examples where it grows like a stretched exponential, with an exponent arbitrarily close to $1$.

Article information

Electron. Commun. Probab., Volume 23 (2018), paper no. 99, 11 pp.

Received: 29 March 2018
Accepted: 12 November 2018
First available in Project Euclid: 19 December 2018

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Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems 37A40: Nonsingular (and infinite-measure preserving) transformations

infinite ergodic theory limit theorems normalization transfer operator renewal Markov chain

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Gouëzel, Sébastien. Growth of normalizing sequences in limit theorems for conservative maps. Electron. Commun. Probab. 23 (2018), paper no. 99, 11 pp. doi:10.1214/18-ECP192. https://projecteuclid.org/euclid.ecp/1545188959

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