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Limit theorems for bivariate Appell polynomials. Part II: Non-central limit theorems
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  • Published: March 1998

Limit theorems for bivariate Appell polynomials. Part II: Non-central limit theorems

  • Liudas Giraitis1,
  • Murad S. Taqqu2 &
  • Norma Terrin3 

Probability Theory and Related Fields volume 110, pages 333–367 (1998)Cite this article

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Summary.

Let (X t ,t∈Z) be a linear sequence with non-Gaussian innovations and a spectral density which varies regularly at low frequencies. This includes situations, known as strong (or long-range) dependence, where the spectral density diverges at the origin. We study quadratic forms of bivariate Appell polynomials of the sequence (X t ) and provide general conditions for these quadratic forms, adequately normalized, to converge to a non-Gaussian distribution. We consider, in particular, circumstances where strong and weak dependence interact. The limit is expressed in terms of multiple Wiener-Itô integrals involving correlated Gaussian measures.

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Authors and Affiliations

  1. Institute of Mathematics and Information, Akademijos 4, 2600 Vilnius, Lithuania (permanent address), , , , , , LT

    Liudas Giraitis

  2. Boston University, Department of Mathematics, 111 Cummington Street, Boston, MA 02215, USA. e-mail: murad@math.bu.edu, , , , , , US

    Murad S. Taqqu

  3. New England Medical Center, 49 Dennet Street, Boston, MA 02111, USA e-mail: norma.terrin@es.nemc.org, , , , , , GB

    Norma Terrin

Authors
  1. Liudas Giraitis
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  2. Murad S. Taqqu
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  3. Norma Terrin
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Received: 22 August 1996 / In revised form: 30 August 1997

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Giraitis, L., Taqqu, M. & Terrin, N. Limit theorems for bivariate Appell polynomials. Part II: Non-central limit theorems. Probab Theory Relat Fields 110, 333–367 (1998). https://doi.org/10.1007/s004400050151

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  • Issue Date: March 1998

  • DOI: https://doi.org/10.1007/s004400050151

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  • Mathematics Subject Classification (1991): 60F05
  • 62M10
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