Consistency of the Takens estimator for the correlation dimension

• 成果类型: Article
• 署名作者: Borovkova, S; Burton, R; Dehling, H
• 署名单位: Oregon State University; University of Groningen
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 1999
• 页码: 376-390
• 关键词: Attractor

摘要

Motivated by the problem of estimating the fractal dimension of a strange attractor, we prove weak consistency of U-statistics for stationary ergodic and mixing sequences when the kernel function is unbounded, extending by this earlier results of Aaronson, Burton, Dehling, Gilat, Hill and Weiss. We apply the obtained results to show consistency of the Takens estimator for the con-elation dimension.