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