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2018 Growth of normalizing sequences in limit theorems for conservative maps
Sébastien Gouëzel
Electron. Commun. Probab. 23: 1-11 (2018). DOI: 10.1214/18-ECP192

Abstract

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 $1$.

Citation

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Sébastien Gouëzel. "Growth of normalizing sequences in limit theorems for conservative maps." Electron. Commun. Probab. 23 1 - 11, 2018. https://doi.org/10.1214/18-ECP192

Information

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

zbMATH: 07023485
MathSciNet: MR3896837
Digital Object Identifier: 10.1214/18-ECP192

Subjects:
Primary: 37A40, 60F05

JOURNAL ARTICLE
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