Central limit theorems for quadratic forms with time-domain conditions

• 成果类型: Article
• 署名作者: Giraitis, L; Taqqu, MS
• 署名单位: Boston University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1998
• 页码: 377-398
• 关键词: long-range dependence; random-variables; gaussian-processes; distributions; SEQUENCES

摘要

We establish the central limit theorem for quadratic forms Sigma(t, s=1)(N) b(t-s)P-m,P- n(X-t, X-s) of the bivariate Appell polynomials P-m,P- n(X-t, X-s) under time-domain conditions. These conditions relate the weights b(t) and the covariances of the sequences (P-m,P- n(X-t, X-s)) and (X-t). The time-domain approach, together with the spectral domain approach developed earlier, yields a general set of conditions for central limit theorems.