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

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Huang, Lorick, Decreusefond, Laurent, Coutin, Laure
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866908927090753536
author Huang, Lorick
Decreusefond, Laurent
Coutin, Laure
author_facet Huang, Lorick
Decreusefond, Laurent
Coutin, Laure
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2401_16834
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Rate of Convergence in the Functional Central Limit Theorem for Stable Processes
Huang, Lorick
Decreusefond, Laurent
Coutin, Laure
Probability
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.
title Rate of Convergence in the Functional Central Limit Theorem for Stable Processes
topic Probability
url https://arxiv.org/abs/2401.16834