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Invariance principles for non-isotropic long memory random fields

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Abstract

We prove that when a random field with bounded spectral density satisfies a Donsker type theorem, its dilated and properly normalised spectral field admits a weak limit. We apply this result to establish the convergence of partial sums for random fields obtained by filtering a white noise. In particular, we prove the convergence of partial sums for strongly-dependent fields whose memory does not satisfy the regularity conditions previously met in the literature.

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Authors and Affiliations

  1. LS-CREST, Paris, France

    Frédéric Lavancier

  2. Université de NANTES, Laboratoire de Mathématiques Jean Leray, UMR CNRS 6629, UFR Sciences et Techniques, 2, rue de la Houssinière, BP 92208, F-44322, NANTES Cedex 3, France

    Frédéric Lavancier

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  1. Frédéric Lavancier
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Correspondence to Frédéric Lavancier.

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Lavancier, F. Invariance principles for non-isotropic long memory random fields. Stat Infer Stoch Process 10, 255–282 (2007). https://doi.org/10.1007/s11203-006-9001-9

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  • DOI: https://doi.org/10.1007/s11203-006-9001-9

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