Nonstandard limit theorem for infinite variance functionals

• 成果类型: Article
• 署名作者: Sly, Allan; Heyde, Chris
• 署名单位: University of California System; University of California Berkeley; Australian National University; Columbia University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/07-AOP345
• 发表日期: 2008
• 页码: 796-805
• 关键词: stable limits; gaussian fields; Moving averages; sums

摘要

We consider functionals of long-range dependent Gaussian sequences with infinite variance and obtain nonstandard limit theorems. When the long-range dependence is strong enough, the limit is a Hermite process, while for weaker long-range dependence, the limit is alpha-stable Levy motion. For the critical value of the long-range dependence parameter, the limit is a sum of a Hermite process and alpha-stable Levy motion.