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

被引：0
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作者：
Liudas Giraitis
Murad S. Taqqu
Norma Terrin
机构：
[1] Institute of Mathematics and Information,
[2] Akademijos 4,undefined
[3] 2600 Vilnius,undefined
[4] Lithuania (permanent address),undefined
[5] Boston University,undefined
[6] Department of Mathematics,undefined
[7] 111 Cummington Street,undefined
[8] Boston,undefined
[9] MA 02215,undefined
[10] USA. e-mail: murad@math.bu.edu,undefined
[11] New England Medical Center,undefined
[12] 49 Dennet Street,undefined
[13] Boston,undefined
[14] MA 02111,undefined
[15] USA e-mail: norma.terrin@es.nemc.org,undefined
来源：
Probability Theory and Related Fields | 1998年 / 110卷
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Mathematics Subject Classification (1991): 60F05; 62M10;
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摘要：
Let (Xt,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 (Xt) 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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页码：333 / 367
页数：34
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