On Eagleson's theorem in the non-stationary setup
Dynamical Systems
2020-11-11 v5 Probability
Abstract
The classical Eagleson's theorem states that if appropriately normalized Birkhoff sums generated by a measurable function and a probability preserving transformation converge in distribution, then they also converge in distribution with respect to any probability measure which is absolutely continuous with respect to the invariant one. In this short note we prove several versions of Eagleson's theorem for some classes of non-stationary stochastic processes which satisfy certain type of decay of correlations.
Cite
@article{arxiv.2004.09333,
title = {On Eagleson's theorem in the non-stationary setup},
author = {Yeor Hafouta},
journal= {arXiv preprint arXiv:2004.09333},
year = {2020}
}
Comments
19 pages; The new version contains results for the iterated WIP