Limit theorems for von Mises statistics of a measure preserving transformation

Manfred Denker, Mikhail Gordin

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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 languageEnglish (US)
Pages (from-to)1-45
Number of pages45
JournalProbability Theory and Related Fields
Volume160
Issue number1-2
DOIs
StatePublished - Oct 2013

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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