Sharp non-asymptotic concentration inequalities for the approximation of the invariant distribution of a diffusion

Igor Honoré

Stochastic Processes and their Applications, 2020, vol. 130, issue 4, 2127-2158

Abstract: Let (Yt)t≥0 be an ergodic diffusion with invariant distribution ν. Consider the empirical measure νn≔(∑k=1nγk)−1∑k=1nγkδXk−1 where (Xk)k≥0 is an Euler scheme with decreasing steps (γk)k≥0 which approximates (Yt)t≥0. Given a test function f, we obtain sharp concentration inequalities for νn(f)−ν(f) which improve the results in Honoré et al. (2019). Our hypotheses on the test function f cover many real applications: either f is supposed to be a coboundary of the infinitesimal generator of the diffusion, or f is supposed to be Lipschitz.

Keywords: Invariant distribution; Diffusion processes; Inhomogeneous Markov chains; Non-asymptotic concentration inequalities (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2019.06.012

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