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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年5月26日

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  • Laure Coutin,
  • Laurent Decreusefond,
  • Lorick Huang

摘要

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.