Limit theorems for von Mises statistics of a measure preserving transformation

• 成果类型: Article
• 署名作者: Denker, Manfred; Gordin, Mikhail
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Scientific Centre of the Russian Academy of Sciences; Saint Petersburg State University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0522-z
• 发表日期: 2014
• 页码: 1-45
• 关键词: U-STATISTICS; INVARIANCE-PRINCIPLES; degenerate; bootstrap

摘要

For a measure preserving transformation of a probability space and some we investigate almost sure and distributional convergence of random variables of the form where C1,C2,...are normalizing constants and the kernel belongs to an appropriate subspace in some . We establish a form of the individual ergodic theorem for such sequences. Using a filtration compatible with and the martingale approximation, we prove a central limit theorem in the non-degenerate case; for a class of canonical (totally degenerate) kernels and , we also show that the convergence holds in distribution towards a quadratic form in independent standard Gaussian variables eta(1), eta(2),....