]. O. Bibliographie-[-bar05 and . Bardou, Contrôle dynamique des erreurs de simulation et d'estimation de processus de diffusion, Thèse de doctorat, 2005.

R. [. Basak and . Bhattacharya, Stability in Distribution for a Class of Singular Diffusions, The Annals of Probability, vol.20, issue.1, pp.312-321, 1992.
DOI : 10.1214/aop/1176989928

. Ph, M. Bressolette, and . Fogli, Quelques méthodes de résolution deprobì emes de dynamique stochastique non linéaire, Ann. Math. Blaise Pascal, vol.1, issue.1, pp.43-60, 1994.

]. 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.

I. [. Basak, C. Hu, and . Wei, Weak convergence of recursions, Stochastic Processes and their Applications, vol.68, issue.1, pp.65-82, 1997.
DOI : 10.1016/S0304-4149(97)00018-5

]. P. Bil99 and . Billingsley, Convergence of probability measures Wiley Series in Probability and Statistics : Probability and Statistics, 1999.

]. F. Cha02 and . Chaabane, Invariance principles with logarithmic averaging for continuous local martingales, Statist. Probab. Lett, vol.59, issue.2, pp.209-217, 2002.

F. Chaabane and F. Maaouia, Th??or??mes limites avec poids pour les martingales vectorielles, ESAIM: Probability and Statistics, vol.4, pp.137-189, 2000.
DOI : 10.1051/ps:2000103

G. [. Douc, E. Fort, and . Moulines, Soulier : Practical drift conditions for subgeometric rates of convergence, Ann. Appl. Probab, vol.14, issue.3, pp.1353-1377, 2004.

M. Duflo, Algorithmes stochastiques, de Mathématiques & Applications (Berlin) [Mathematics & Applications, 1996.

M. Duflo, Random iterative models, de Applications of Mathematics, 1997.
DOI : 10.1007/978-3-662-12880-0

T. [. Ethier and . Kurtz, Markov processes Wiley Series in Probability and Mathematical Statistics : Probability and Mathematical Statistics, 1986.

]. O. Fau92 and . Faure, Simulation du mouvement brownien et des diffusions, Thèse de doctorat, ´ Ecole nationale des ponts et chaussées, 1992.

]. W. Fel52 and . Feller, The parabolic differential equations and the associated semi-groups of transformations, Ann. of Math, vol.55, issue.2, pp.468-519, 1952.

]. W. Fel54 and . Feller, Diffusion processes in one dimension, Trans. Amer. Math. Soc, vol.77, pp.1-31, 1954.

M. I. Gordin and B. A. Lif?ic, Central limit theorem for stationary Markov processes, Dokl. Akad. Nauk SSSR, vol.239, issue.4, pp.766-767, 1978.

H. Ganidis, B. Roynette, and F. Simonot, Convergence rate of some semi-groups to their invariant probability, Stochastic Processes and their Applications, vol.79, issue.2, pp.243-263, 1999.
DOI : 10.1016/S0304-4149(98)00084-2

]. R. Has80, Has ? minski? ? : Stochastic stability of differential equations, volume 7 de Monographs and Textbooks on Mechanics of Solids and Fluids : Mechanics and Analysis. Sijthoff & Noordhoff, Alphen aan den Rijn, 1980.

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

W. [. Ibrahim and . Li, Principal internal resonances in 3-dof systems subjected to wide-band random excitation, J. Sound Vibration, vol.131, issue.2, pp.305-321, 1989.

K. Itô, H. P. Mckean, and J. , Diffusion processes and their sample paths, 1974.

I. Karatzas and S. E. Shreve, Brownian motion and stochastic calculus, volume 113 de Graduate Texts in Mathematics, 1991.

S. Karlin and H. M. Taylor, A second course in stochastic processes, 1981.

H. Lamba, J. Mattingly, and A. M. Stuart, Strong convergence of an adaptive euler-maruyama scheme for stochastic differential equations i, 2003.

D. Lamberton, Pagès : Recursive computation of the invariant distribution of a diffusion, Bernoulli, vol.8, issue.3, pp.367-405, 2002.

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

L. Ljung and G. Pflug, Walk : Stochastic approximation and optimization of random systems, volume 17 de DMV Seminar, 1992.

]. F. Maa01 and . Maaoui, Principes d'invariance par moyennisation logarithmique pour les processus de Markov, Ann. Probab, vol.29, issue.4, pp.1859-1902, 2001.

J. C. Mattingly and A. M. Stuart, Strong convergence of an adaptive eulermaruyama scheme for stochastic differential equations ii, 2004.

J. C. Mattingly, A. M. Stuart, and D. J. Higham, Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise, Stochastic Processes and their Applications, vol.101, issue.2, pp.185-232, 2002.
DOI : 10.1016/S0304-4149(02)00150-3

]. G. Pag01 and . Pagès, Sur quelques algorithmes récursifs pour les probabilités numériques, ESAIM Probab. Statist, vol.5, pp.141-170, 2001.

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

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

. [. Rogers, Williams : Diffusions, Markov processes, and martingales, Wiley Series in Probability and Mathematical Statistics : Probability and Mathematical Statistics, 1994.

D. Revuz, Yor : Continuous martingales and Brownian motion, de Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 1999.
DOI : 10.1007/978-3-662-06400-9

]. C. Soi94 and . Soize, The Fokker-Planck equation for stochastic dynamical systems and its explicit steady state solutions, de Series on Advances in Mathematics for Applied Sciences, 1994.

W. F. Stout, Almost sure convergence Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], Probability and Mathematical Statistics, vol.24, 1974.

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

]. D. Tal02 and . Talay, Stochastic Hamiltonian systems : exponential convergence to the invariant measure, and discretization by the implicit Euler scheme Inhomogeneous random systems, Markov Process . Related Fields, pp.163-198, 2001.