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arXiv · 1803.11450

Variations around Eagleson's Theorem on mixing limit theorems for dynamical systems

Sébastien Gouëzel
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Abstract

Eagleson's Theorem asserts that, given a probability-preserving map, ifrenormalized Birkhoff sums of a function converge in distribution, thenthey also converge with respect to any probability measure which isabsolutely continuous with respect to the invariant one. We prove a versionof this result for almost sure limit theorems, extending results ofKorepanov. We also prove a version of this result, in mixing systems, whenone imposes a conditioning both at time 0 and at time n.

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Sébastien Gouëzel. 2018-03-30. Variations around Eagleson's Theorem on mixing limit theorems for dynamical systems. https://arxiv.org/abs/1803.11450

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