Quenched normal approximation for random sequences of transformations
Dynamical Systems
2020-01-08 v1 Probability
Abstract
We study random compositions of transformations having certain uniform fiberwise properties and prove bounds which in combination with other results yield a quenched central limit theorem equipped with a convergence rate, also in the multivariate case, assuming fiberwise centering. For the most part we work with non-stationary randomness and non-invariant, non-product measures. Independently, we believe our work sheds light on the mechanisms that make quenched central limit theorems work, by dissecting the problem into three separate parts.
Cite
@article{arxiv.1810.10760,
title = {Quenched normal approximation for random sequences of transformations},
author = {Olli Hella and Mikko Stenlund},
journal= {arXiv preprint arXiv:1810.10760},
year = {2020}
}