]. R. Bha82 and . Bhattacharya, On the functional central limit theorem and the law of the iterated logarithm for Markov processes, Z. Wahrsch. Verw. Gebiete, vol.60, issue.2, pp.185-201, 1982.

P. Billingsley, Ergodic theory and information. Robert E, 1978.

A. [. Dalalyan and . Tsybakov, Sparse regression learning by aggregation and Langevin Monte-Carlo, Journal of Computer and System Sciences, vol.78, issue.5, pp.1423-1443, 2012.
DOI : 10.1016/j.jcss.2011.12.023

URL : https://hal.archives-ouvertes.fr/hal-00362471

]. N. Fri16 and . Frikha, Multi-level stochastic approximation algorithms, Ann. Appl. Probab, vol.26, issue.2, pp.933-985, 2016.

M. B. Giles, Multilevel Monte Carlo Path Simulation, Operations Research, vol.56, issue.3, pp.607-617, 2008.
DOI : 10.1287/opre.1070.0496

D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 1983.

. [. García-trillos, A decreasing step method for strongly oscillating stochastic models, The Annals of Applied Probability, vol.25, issue.2, pp.986-1029, 2015.
DOI : 10.1214/14-AAP1016

C. [. Hall and . Heyde, Martingale limit theory and its application, Probability and Mathematical Statistics, 1980.

]. U. Kre85 and . Krengel, Ergodic theorems, 1985.

]. V. Lem05 and . Lemaire, Estimation récursive de la mesure invariante d'un processus de diffusion, Thèse de doctorat, 2005.

]. V. Lem07 and . Lemaire, Behavior of the Euler scheme with decreasing step in a degenerate situation, ESAIM Probab. Stat, vol.11, pp.236-247, 2007.

D. Lamberton and G. Pagès, Recursive computation of the invariant distribution of a diffusion, Bernoulli, vol.8, issue.3, pp.367-405, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00104799

D. Lamberton and G. Pagès, RECURSIVE COMPUTATION OF THE INVARIANT DISTRIBUTION OF A DIFFUSION: THE CASE OF A WEAKLY MEAN REVERTING DRIFT, Stochastics and Dynamics, vol.03, issue.04, pp.435-451, 2003.
DOI : 10.1142/S0219493703000838

URL : https://hal.archives-ouvertes.fr/hal-00104799

G. [. Lemaire and . Pagès, Multilevel Richardson-Romberg Extrapolation, SSRN Electronic Journal, p.2013
DOI : 10.2139/ssrn.2539114

URL : https://hal.archives-ouvertes.fr/hal-00920660

G. [. Lemaire, F. Pagès, and . Panloup, Invariant measure of duplicated diffusions and application to Richardson???Romberg extrapolation, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.51, issue.4, pp.1562-1596, 2015.
DOI : 10.1214/13-AIHP591

URL : https://hal.archives-ouvertes.fr/hal-01245443

]. G. Pag07 and . Pagès, Multi-step Richardson-Romberg extrapolation: remarks on variance control and complexity, Monte Carlo Methods Appl, vol.13, issue.1, pp.37-70, 2007.

]. F. Pan08 and . Panloup, Recursive computation of the invariant measure of a stochastic differential equation driven by a Lévy process, Annals of Applied Probability, vol.18, issue.2, pp.379-426, 2008.

G. Pagès and F. Panloup, Approximation of the distribution of a stationary Markov process with application to option pricing, Bernoulli, vol.15, issue.1, pp.146-177, 2009.
DOI : 10.3150/08-BEJ142

G. Pagès and F. Panloup, A mixed-step algorithm for the approximation of the stationary regime of a diffusion, Stochastic Processes and their Applications, vol.124, issue.1, pp.522-565, 2014.
DOI : 10.1016/j.spa.2013.07.011

M. Piccioni and S. Scarlatti, An Iterative Monte Carlo Scheme for Generating Lie Group-Valued Random Variables, Advances in Applied Probability, vol.37, issue.03, pp.616-628, 1994.
DOI : 10.1214/aop/1176990228

A. [. Pardoux, . Yu, and . Veretennikov, On the Poisson equation and diffusion approximation. I. Ann, Probab, vol.29, issue.3, pp.1061-1085, 2001.

]. D. Tal90 and . Talay, Second order discretization schemes of stochastic differential systems for the computation of the invariant law, Stoch. Stoch. Rep, vol.29, issue.1, pp.13-36, 1990.