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

math. arxive. Cornell University, 2016. No. 1605.08525.
Honoré I., Menozzi S.
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) Fr{\"o}benius 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.