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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https://hal.archives-ouvertes.fr/hal-01321645
Contributor : Stephane Menozzi <>
Submitted on : Wednesday, May 23, 2018 - 5:47:39 PM
Last modification on : Wednesday, May 15, 2019 - 3:51:47 AM
Long-term archiving on : Saturday, August 25, 2018 - 12:20:48 AM

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  • HAL Id : hal-01321645, version 4
  • 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. 2018. ⟨hal-01321645v4⟩

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