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

Autor: Huang, Lorick, Decreusefond, Laurent, Coutin, Laure
Rok vydání: 2024
Předmět:
Druh dokumentu: Working Paper
Popis: 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.
Databáze: arXiv