On the asymptotic distributions of partial, sums of functionals of infinite-variance moving averages

• 成果类型: Article
• 署名作者: Hsing, T
• 署名单位: National University of Singapore; Texas A&M University System; Texas A&M University College Station
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1022677460
• 发表日期: 1999
• 页码: 1579-1599
• 关键词: CENTRAL LIMIT-THEOREMS; gaussian fields; CONVERGENCE

摘要

This paper investigates the asymptotic distribution of the partial sum S-N = Sigma(n=1)(N)[K(X-n) - EK(X-n)], as N --> infinity, where {X-n} is a moving average stable process and K is a bounded and measurable function. The results show that SN follows a central or non-central limit theorem depending on the rate at which the moving average coefficients tend to 0.