Rate of Convergence in the Functional Central Limit Theorem for Stable Processes
Probability
2026-04-02 v1
Abstract
In this article, we quantify the functional convergence of the rescaled random walk with heavy tails to a stable process.This generalizes the Generalized Central Limit Theorem for stable random variables infinite dimension. We show that provided we have a control between the randomwalk or the limiting stable process and their respective affine interpolation, we canlift the rate of convergence obtained for multivariate distributions to a rateof convergence in some functional spaces.
Keywords
Cite
@article{arxiv.2401.16834,
title = {Rate of Convergence in the Functional Central Limit Theorem for Stable Processes},
author = {Lorick Huang and Laurent Decreusefond and Laure Coutin},
journal= {arXiv preprint arXiv:2401.16834},
year = {2026}
}