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

• 成果类型: Article
• 署名作者: Giraitis, L; Taqqu, MS; Terrin, N
• 署名单位: Vilnius University; Boston University; Tufts Medical Center
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s004400050151
• 发表日期: 1998
• 页码: 333-367
• 关键词: long-range dependence; quadratic-forms; CONVERGENCE; variables

摘要

Let (X-t, t is an element of 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-Ito integrals involving correlated Gaussian measures.