Central limit theorem for stationary linear processes

• 成果类型: Article
• 署名作者: Peligrad, Magda; Utev, Sergey
• 署名单位: University System of Ohio; University of Cincinnati; University of Nottingham
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000179
• 发表日期: 2006
• 页码: 1608-1622
• 关键词: dependent random-variables; invariance-principle; functionals

摘要

We establish the central limit theorem for linear processes with dependent innovations including martingales and mixingale type of assumptions as defined in McLeish [Ann. Probab. 5 (1977) 616-621] and motivated by Gordin [Soviet Math. Dokl. 10 (1969) 1174-1176]. In doing so we shall preserve the generality of the coefficients, including the long range dependence case, and we shall express the variance of partial sums in a form easy to apply. Ergodicity is not required.