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arXiv · 1810.10760

Quenched normal approximation for random sequences of transformations

Olli Hella·Mikko Stenlund
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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.

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Olli Hella, Mikko Stenlund. 2018-10-25. Quenched normal approximation for random sequences of transformations. https://doi.org/10.1007/s10955-019-02390-5

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