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) |
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Pages (from-to) | 1-45 |
Number of pages | 45 |
Journal | Probability Theory and Related Fields |
Volume | 160 |
Issue number | 1-2 |
DOIs | |
State | Published - Oct 2013 |
All Science Journal Classification (ASJC) codes
- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty