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

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  • Honoré, Igor

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.

Suggested Citation

  • Honoré, Igor, 2020. "Sharp non-asymptotic concentration inequalities for the approximation of the invariant distribution of a diffusion," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2127-2158.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:4:p:2127-2158
    DOI: 10.1016/j.spa.2019.06.012
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    References listed on IDEAS

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    1. Panloup, Fabien, 2008. "Computation of the invariant measure for a Lévy driven SDE: Rate of convergence," Stochastic Processes and their Applications, Elsevier, vol. 118(8), pages 1351-1384, August.
    2. Basak, Gopal K. & Hu, Inchi & Wei, Ching-Zong, 1997. "Weak convergence of recursions," Stochastic Processes and their Applications, Elsevier, vol. 68(1), pages 65-82, May.
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