PreprintCC BY-NC 4.0HAL
Stein's functional method for weakly dependent random variables
Abstract
This article extends Stein's functional method to establish explicit rates of convergence in the Wasserstein-1 distance for Donsker's invariance principle under weak dependence. Our approach first reduces the problem of bounding distances between distributions on a function space to estimating distances between finite-dimensional marginals. We then employ the block technique, which is standard in Stein's methodology, to handle dependence. While our analysis focuses on φ-mixing sequences, the method extends to other forms of weak dependence admitting suitable covariance inequalities.
Related
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BibTeX
@misc{coutin2026steins,
title = {{Stein's functional method for weakly dependent random variables}},
author = {Laure Coutin and Sérigné Darou Kebe and Laurent Decreusefond},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24704},
eprint = {2609.24704},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05755223v1},
note = {CC BY-NC 4.0},
}
RIS
TY - UNPB
TI - Stein's functional method for weakly dependent random variables
AU - Laure Coutin
AU - Sérigné Darou Kebe
AU - Laurent Decreusefond
PY - 2026
DA - 2026/09/18
PB - HAL
DO - 10.48550/arxiv.2609.24704
UR - https://hal.science/hal-05755223v1
AB - This article extends Stein's functional method to establish explicit rates of convergence in the Wasserstein-1 distance for Donsker's invariance principle under weak dependence. Our approach first reduces the problem of bounding distances between distributions on a function space to estimating distances between finite-dimensional marginals. We then employ the block technique, which is standard in Stein's methodology, to handle dependence. While our analysis focuses on φ-mixing sequences, the method extends to other forms of weak dependence admitting suitable covariance inequalities.
ER -