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Stein's method for Brownian approximations

Abstract : Motivated by a theorem of Barbour, we revisit some of the classical limit theorems in probability from the viewpoint of the Stein method. We setup the framework to bound Wasserstein distances between some distributions on infinite dimensional spaces. We show that the convergence rate for the Poisson approximation of the Brownian motion is as expected proportional to $\lambda^{-1/2}$ where $\lambda$ is the intensity of the Poisson process. We also exhibit the speed of convergence for the Donsker Theorem and for the linear interpolation of the Brownian motion. By iterating the procedure, we give Edgeworth expansions with precise error bounds.
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Contributor : Laurent Decreusefond Connect in order to contact the contributor
Submitted on : Friday, September 20, 2013 - 10:19:53 AM
Last modification on : Monday, April 4, 2022 - 3:24:12 PM
Long-term archiving on: : Friday, April 7, 2017 - 12:21:33 AM


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  • HAL Id : hal-00717812, version 2
  • ARXIV : 1207.3517


Laure Coutin, Laurent Decreusefond. Stein's method for Brownian approximations. Communications on Stochastic Analysis, 2013, 7 (3), pp.349-372. ⟨hal-00717812v2⟩



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