Rate of Convergence in the Functional Central Limit Theorem for Stable Processes

2024/01/30 by Huang, Lorick, Decreusefond, Laurent, Coutin, Laure
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2401.16834

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.

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