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Stable limits for associated regularly varying sequences

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Abstract

For a stationary sequence that is regularly varying and associated, we give conditions guaranteeing that partial sums of this sequence, under normalization related to the exponent of regular variation, converge in distribution to a stable non-Gaussian limit. The obtained limit theorem admits a natural extension to the functional convergence in Skorokhod’s M1 topology.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100, Toruń, Poland

    Adam Jakubowski

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  1. Adam Jakubowski
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Correspondence to Adam Jakubowski.

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Dedicated to Professor Vygantas Paulauskas on the occasion of his 75th birthday

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Jakubowski, A. Stable limits for associated regularly varying sequences. Lith Math J 59, 535–544 (2019). https://doi.org/10.1007/s10986-019-09463-8

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  • DOI: https://doi.org/10.1007/s10986-019-09463-8

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