Non-asymptotic Gaussian estimates for the recursive approximation of the invariant distribution of a diffusion
| Autor: | Igor Honoré, Stéphane Menozzi, Gilles Pagès |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Gaussian Matrix norm 01 natural sciences 010104 statistics & probability symbols.namesake Ergodic theory Applied mathematics Infinitesimal generator 0101 mathematics Diffusion processes Inhomogeneous Markov chains Brownian motion Mathematics Central limit theorem Almost sure Central Limit Theorem 010102 general mathematics Empirical distribution function 35J15 symbols 60H35 Invariant measure Statistics Probability and Uncertainty 60E15 Invariant distribution Non-asymptotic Gaussian concentration |
| Zdroj: | Ann. Inst. H. Poincaré Probab. Statist. 56, no. 3 (2020), 1559-1605 |
| Popis: | We obtain non-asymptotic Gaussian concentration bounds for the difference between the invariant distribution $\nu $ 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 $f-\nu (f)$ is a coboundary of the infinitesimal generator. We show that these bounds can still be improved when some suitable squared-norms of the diffusion coefficient also belong to this class. We apply these estimates 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. |
| Databáze: | OpenAIRE |
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