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Invariance principles for some FARIMA and nonstationary linear processes in the domain of a stable distribution
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  • Published: 26 June 2011

Invariance principles for some FARIMA and nonstationary linear processes in the domain of a stable distribution

  • Ph. Barbe1 &
  • W. P. McCormick2 

Probability Theory and Related Fields volume 154, pages 429–476 (2012)Cite this article

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Abstract

We prove some invariance principles for processes which generalize FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution. The limiting processes are extensions of the fractional Lévy processes. The technique used is interesting in itself; it extends an older idea of splitting a sample into a central part and an extreme one, analyzing each part with different techniques, and then combining the results. This technique seems to have the potential to be useful in other problems in the domain of nonGaussian stable distributions.

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Author information

Authors and Affiliations

  1. CNRS (UMR 8088), 90 rue de Vaugirard, 75006, Paris, France

    Ph. Barbe

  2. Department of Statistics, University of Georgia, Athens, GR, 30602, USA

    W. P. McCormick

Authors
  1. Ph. Barbe
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  2. W. P. McCormick
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Corresponding author

Correspondence to W. P. McCormick.

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Barbe, P., McCormick, W.P. Invariance principles for some FARIMA and nonstationary linear processes in the domain of a stable distribution. Probab. Theory Relat. Fields 154, 429–476 (2012). https://doi.org/10.1007/s00440-011-0374-3

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  • Received: 16 July 2010

  • Revised: 13 February 2011

  • Published: 26 June 2011

  • Issue Date: December 2012

  • DOI: https://doi.org/10.1007/s00440-011-0374-3

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Keywords

  • Invariance principle
  • NonGaussian stable distribution
  • FARIMA processes
  • Fractional Lévy stable process
  • Fractional Brownian motion
  • Generalized integrated process

Mathematics Subject Classification (2010)

  • Primary: 60F17
  • Secondary: 60G22
  • 60G52
  • 60G55
  • 60G50
  • 62M10
  • 62G32
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