Limit theorems for bivariate Appell polynomials. Part II: Non-central limit theorems |
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| Authors: | Liudas Giraitis Murad S Taqqu Norma Terrin |
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| Institution: | (1) Institute of Mathematics and Information, Akademijos 4, 2600 Vilnius, Lithuania (permanent address), LT;(2) Boston University, Department of Mathematics, 111 Cummington Street, Boston, MA 02215, USA. e-mail: murad@math.bu.edu, US;(3) New England Medical Center, 49 Dennet Street, Boston, MA 02111, USA e-mail: norma.terrin@es.nemc.org, GB |
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| Abstract: | 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-It? integrals involving correlated Gaussian measures.
Received: 22 August 1996 / In revised form: 30 August 1997 |
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| Keywords: | Mathematics Subject Classification (1991): 60F05 62M10 |
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