@article{bd173a2e4ac34b1c8121c6f1b31194fd,
title = "Limit theorems for von Mises statistics of a measure preserving transformation",
abstract = "For a measure preserving transformation We establish a form of the individual ergodic theorem for such sequences. Using a filtration compatible with T and the martingale approximation, we prove a central limit theorem in the non-degenerate case; for a class of canonical (totally degenerate) kernels and d = 2, we also showthat the convergence holds in distribution towards a quadratic form.",
author = "Manfred Denker and Mikhail Gordin",
note = "Funding Information: The authors would like to thank Herold Dehling for several discussions clarifying many aspects of limit distributions for -statistics and for his encouragement to get this paper written. Also comments by referees were very helpful. The research was supported by the Deutsche Forschungsgemeinschaft under Grant Number 436 RUS 113/962/0-1 and the Russian Foundation for Basic Research under Grant Number 09-01-91331-NNIO-a. Manfred Denker was also partially supported by the National Science Foundation under Grant Number DMS-10008538. Mikhail Gordin was also partially supported by the Grant Number 13-01-00256-a of the Russian Foundation for Basic Research and by the grant Number NS-1216.2012.1 for the Support of Scientific Schools. He thanks Axel Munk (Institute for Mathematical Stochastics) and Laurent Bartholdi (Mathematical Institute) for their hospitality at the University of G{\"o}ttingen where a part of this paper was prepared. Publisher Copyright: {\textcopyright} 2013, Springer-Verlag Berlin Heidelberg.",
year = "2013",
month = oct,
doi = "10.1007/s00440-013-0522-z",
language = "English (US)",
volume = "160",
pages = "1--45",
journal = "Probability Theory and Related Fields",
issn = "0178-8051",
publisher = "Springer New York",
number = "1-2",
}