On the central limit theorem for stationary random fields under L 1 -projective condition

Han-Mai Lin; Florence Merlevède; Dalibor Voln{ý}

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arXiv · 2201.06798

On the central limit theorem for stationary random fields under L 1 -projective condition

Han-Mai Lin·Florence Merlevède·Dalibor Voln{ý}

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Abstract

The first aim of this paper is to wonder to what extent we can generalize the central limit theorem of Gordin [5] under the so-called L 1-projective criteria to ergodic stationary random fields when completely commuting filtrations are considered. Surprisingly it appears that this result cannot be extended to its full generality and that an additional condition is needed.

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Han-Mai Lin, Florence Merlevède, Dalibor Voln{ý}. 2022-01-18. On the central limit theorem for stationary random fields under L 1 -projective condition. https://arxiv.org/abs/2201.06798

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