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2022 On the central limit theorem for stationary random fields under L1-projective condition
Han-Mai Lin, Florence Merlevède, Dalibor Volný
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Electron. Commun. Probab. 27: 1-12 (2022). DOI: 10.1214/22-ECP486

Abstract

The first aim of this paper is to wonder to what extent we can generalize the central limit theorem of Gordin [6] under the so-called L1-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.

Acknowledgments

The authors are grateful to the referee for his useful remarks.

Citation

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Han-Mai Lin. Florence Merlevède. Dalibor Volný. "On the central limit theorem for stationary random fields under L1-projective condition." Electron. Commun. Probab. 27 1 - 12, 2022. https://doi.org/10.1214/22-ECP486

Information

Received: 3 March 2022; Accepted: 11 September 2022; Published: 2022
First available in Project Euclid: 23 September 2022

Digital Object Identifier: 10.1214/22-ECP486

Subjects:
Primary: 60F05 , 60G60

Keywords: central limit theorem , co-boundary decomposition , ortho-martingale , Projective criteria , stationary random fields

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