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Asymptotic Normality in Banach Spaces via Lindeberg Method

Author

Listed:
  • Alfredas Račkauskas

    (Vilnius University)

  • Charles Suquet

    (Univ. Lille, CNRS, UMR 8524 - Laboratoire Paul Painlevé)

Abstract

The relation between weak convergence of probabilities on a smooth Banach space and uniform convergence over a certain class of smooth functions is established. This leads to an extension of Lindeberg’s proof of the central limit theorem in a Banach space framework. As a result, asymptotic normality is proved for sums of Banach space random variables including triangular arrays and weighted linear processes.

Suggested Citation

  • Alfredas Račkauskas & Charles Suquet, 2023. "Asymptotic Normality in Banach Spaces via Lindeberg Method," Journal of Theoretical Probability, Springer, vol. 36(1), pages 409-455, March.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:1:d:10.1007_s10959-022-01177-x
    DOI: 10.1007/s10959-022-01177-x
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    References listed on IDEAS

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