Limit theorems for von Mises statistics of a measure preserving transformation

Manfred Denker; Mikhail Gordin

doi:10.1007/s00440-013-0522-z

Limit theorems for von Mises statistics of a measure preserving transformation

Manfred Denker, Mikhail Gordin

Research output: Contribution to journal › Article › peer-review

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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.

Original language	English (US)
Pages (from-to)	1-45
Number of pages	45
Journal	Probability Theory and Related Fields
Volume	160
Issue number	1-2
DOIs	https://doi.org/10.1007/s00440-013-0522-z
State	Published - Oct 2013

All Science Journal Classification (ASJC) codes

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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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.",

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AB - 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.

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Limit theorems for von Mises statistics of a measure preserving transformation

Abstract

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