Non-Asymptotic Gaussian Estimates for the Recursive Approximation of the Invariant Measure of a Diffusion

Abstract : We obtain non-asymptotic Gaussian concentration bounds for the difference between the invariant measure ν of an ergodic Brownian diffusion process and the empirical distribution of an approximating scheme with decreasing time step along a suitable class of (smooth enough) test functions f such that f − ν(f) is a coboundary of the infinitesimal generator. We show that these bounds can still be improved when the (squared) Fröbenius norm of the diffusion coefficient lies in this class. We apply these bounds to design computable non-asymptotic confidence intervals for the approximating scheme. As a theoretical application, we finally derive non-asymptotic deviation bounds for the almost sure Central Limit Theorem.
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Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01321645
Contributeur : Stephane Menozzi <>
Soumis le : lundi 10 juillet 2017 - 21:12:37
Dernière modification le : vendredi 28 juillet 2017 - 01:10:49

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  • HAL Id : hal-01321645, version 3
  • ARXIV : 1605.08525

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Igor Honoré, Stephane Menozzi, Gilles Pagès. Non-Asymptotic Gaussian Estimates for the Recursive Approximation of the Invariant Measure of a Diffusion. 2017. 〈hal-01321645v3〉

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