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.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty