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Preprints, Working Papers, ... Year : 2024

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

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 in finite dimension. We show that provided we have a control between the random walk or the limiting stable process and their respective affine interpolation, we can lift the rate of convergence obtained for multivariate distributions to a rate of convergence in some functional spaces.
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Dates and versions

hal-04424279 , version 1 (29-01-2024)

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Lorick Huang, Laurent Decreusefond, Laure Coutin. Rate of Convergence in the Functional Central Limit Theorem for Stable Processes. 2024. ⟨hal-04424279⟩
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