V. Bally and D. Talay, The law of the Euler scheme for stochastic differential equations, Probability Theory and Related Fields, vol.8, issue.1, pp.43-60, 1995.
DOI : 10.1007/978-3-662-12616-5
URL : https://hal.archives-ouvertes.fr/inria-00074427

V. Bally and D. Talay, The Law of the Euler Scheme for Stochastic Differential Equations: II. Convergence Rate of the Density, Monte Carlo Methods and Applications, vol.2, issue.2, pp.93-128, 1996.
DOI : 10.1515/mcma.1996.2.2.93
URL : https://hal.archives-ouvertes.fr/inria-00074016

M. Bossy, E. Gobet, and D. Talay, A symmetrized Euler scheme for an efficient approximation of reflected diffusions, J. Appl. Prob, vol.41, pp.877-889, 2004.

P. Cattiaux, Stochastic calculus and degenerate boundary value problems, Annales de l???institut Fourier, vol.42, issue.3, pp.541-624, 1992.
DOI : 10.5802/aif.1302
URL : http://archive.numdam.org/article/AIF_1992__42_3_541_0.pdf

P. Cattiaux, J. R. Leon, and C. Prieur, Estimation for stochastic damping hamiltonian systems under partial observation???I. Invariant density, Proc. and their Appli, pp.1236-1260, 2014.
DOI : 10.1016/j.spa.2013.10.008
URL : https://hal.archives-ouvertes.fr/hal-00739136

J. Dedecker and C. Prieur, New dependence coefficients. Examples and applications to statistics. Probab. Theory and Relat, pp.203-236, 2005.

P. Doukhan, Mixing. Properties and examples, Lecture Notes in Statistics, vol.85, 1994.

E. Gobet, Euler schemes and half-space approximation for the simulation of diffusion in a domain, ESAIM: Probability and Statistics, vol.8, issue.4, pp.261-297, 2001.
DOI : 10.1016/0304-4149(94)90118-X

E. Gobet, Efficient schemes for the weak approximation of reflected diffusions, Monte Carlo Methods and Applications, vol.7, issue.1-2, pp.193-202, 2001.
DOI : 10.1515/mcma.2001.7.1-2.193

E. Gobet and C. Labart, Sharp estimates for the convergence of the density of the Euler scheme in small time, Electronic Communications in Probability, vol.13, issue.0, pp.352-363, 2008.
DOI : 10.1214/ECP.v13-1393
URL : https://hal.archives-ouvertes.fr/hal-00281365

J. Guyon, Euler scheme and tempered distributions, Stoch. Proc. and their Appli, pp.877-904, 2006.
DOI : 10.1016/j.spa.2005.11.011
URL : https://doi.org/10.1016/j.spa.2005.11.011

I. Honoré, S. Menozzi, and G. Pagès, Non asymptotic Gaussian estimates for the recursive approximation of the invariant measure of a diffusion, 2016.

N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, 1981.

J. C. Mattingly, A. M. Stuart, and D. J. Higham, Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise, Stoch. Proc. and their Appli. 101, pp.185-232, 2002.
DOI : 10.1016/S0304-4149(02)00150-3
URL : https://doi.org/10.1016/s0304-4149(02)00150-3

S. Meyn and R. Tweedie, Markov chains and stochastic stability, 2009.

T. Shardlow and A. M. Stuart, A Perturbation Theory for Ergodic Markov Chains and Application to Numerical Approximations, SIAM Journal on Numerical Analysis, vol.37, issue.4, pp.1120-1137, 2000.
DOI : 10.1137/S0036142998337235

D. Talay, Second-order discretization schemes of stochastic differential systems for the computation of the invariant law, Stochastics and Stochastic Reports, vol.20, issue.1, pp.13-36, 1990.
DOI : 10.1017/S0021900200097072
URL : https://hal.archives-ouvertes.fr/inria-00075799

M. Valera-lópez, A. Pineda, J. R. León, and H. Id, Application of satellite image to the implementation of two stochastic models for modeling the transport of chlorophyll-a on Lake Valencia (Venezuela), p.1293471, 2016.

C. Patrick and I. De-mathématiques-de-toulouse, CNRS UMR 5219., 118 route de Narbonne, 31062 Toulouse cedex 09, France. E-mail address: cattiaux@math.univ-toulouse.fr José LÉ ON E-mail address: jose.leon@ciens.ucv.ve Clémentine PRIEUR