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

Lorick Huang; Laurent Decreusefond; Laure Coutin

doi:10.1007/s11118-025-10215-2

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arXiv · 2401.16834

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

Lorick Huang·Laurent Decreusefond·Laure Coutin

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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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Lorick Huang, Laurent Decreusefond, Laure Coutin. 2024-01-30. Rate of Convergence in the Functional Central Limit Theorem for Stable Processes. https://doi.org/10.1007/s11118-025-10215-2

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