Limit theorems for von Mises statistics of a measure preserving transformation

作者：Denker Manfred^*; Gordin Mikhail

来源：Probability Theory and Related Fields, 2014, 160(1-2): 1-45.

DOI：10.1007/s00440-013-0522-z

• Von Mises statistic
• Measure preserving transformation
• Projective tensor product
• Ergodic theorem
• Hoeffding decomposition
• Central limit theorem
• Martingale approximation

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),....

• 出版日期2014-10