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Wasserstein convergence rates in the invariance principle for sequential dynamical systems

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arxiv 2307.13913 v2 pith:WFLUY7FJ submitted 2023-07-26 math.DS

Zhenxin Liu , Zhe Wang This is my paper · ORCID
classification math.DS
keywords dynamicalsequentialsystemscaseconvergenceinvarianceprinciplewasserstein
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abstract

In this paper, we consider the convergence rate with respect to the Wasserstein distance in the invariance principle for sequential dynamical systems. We utilize and modify the techniques previously employed for stationary sequences to address our non-stationary case. Under certain assumptions, we can apply our result to a large class of dynamical systems, including sequential $\beta_n$-transformations, piecewise uniformly expanding maps with additive noise in one-dimensional and multidimensional case, and so on.

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Cited by 1 Pith paper

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  1. Prokhorov Metric Convergence of the Partial Sum Process for Reconstructed Functional Data

    math.ST 2025-06 conditional novelty 7.0 of 10

    For dependent, approximately stationary random functions in C0, the partial sum process is within O(N^{-τ}) of a functional Brownian motion in Prokhorov and Wasserstein distance.

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