]. R. Bas97 and . Bass, Diffusions and Elliptic Operators, 1997.

G. Sergey, I. Bobkov, M. Gentil, and . Ledoux, Hypercontractivity of Hamilton-Jacobi equations, J. Math. Pures Appl, vol.80, issue.97, pp.669-696, 2001.

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.104-143, 1996.
DOI : 10.1007/BF01303802

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 Appl, J. M. Coron. Control and nonlinearity. Mathematical Surveys and Monographs, vol.2, issue.136, pp.93-128, 1996.
URL : https://hal.archives-ouvertes.fr/inria-00074016

F. Delarue and S. Menozzi, Density estimates for a random noise propagating through a chain of differential equations, Fri75] A. Friedman. Stochastic differential equations. Chapmann-Hall, 1975.
DOI : 10.1016/j.jfa.2010.05.002

URL : https://hal.archives-ouvertes.fr/hal-00436051

E. Gobet and C. Labart, Sharp estimates for the convergence of the density of the Euler scheme in small time, JO09] A. Joulin and Y. Ollivier. Curvature, concentration, and error estimates for Markov chain Monte Carlo, pp.352-3631312, 2008.
DOI : 10.1214/ECP.v13-1393

URL : https://hal.archives-ouvertes.fr/hal-00281365

V. Konakov and E. Mammen, Local limit theorems for transition densities of Markov chains converging to diffusions, Probability Theory and Related Fields, vol.117, issue.4, pp.551-587, 2000.
DOI : 10.1007/PL00008735

V. Konakov and E. Mammen, Edgeworth type expansions for Euler schemes for stochastic differential equations., Monte Carlo Methods and Applications, vol.8, issue.3, pp.8-3271, 2002.
DOI : 10.1515/mcma.2002.8.3.271

V. Konakov, S. Menozzi, S. N. Molchanovkol34-]-a, and . Kolmogorov, Explicit parametrix and local limit theorems for some degenerate diffusion processes Zufällige Bewegungen (zur Theorie der Brownschen Bewegung), KS87] S. Kusuoka and D. Stroock. Applications of the Malliavin calculus Concentration of measure and logarithmic sobolev inequalities. Séminaire de Probabilités XXXIII. LNM, 1709, pp.2-35116, 1934.
DOI : 10.1214/09-aihp207

URL : http://arxiv.org/abs/0802.2229

H. P. Mckean and I. M. Singer, Curvature and the eigenvalues of the Laplacian, Journal of Differential Geometry, vol.1, issue.1-2, pp.43-69, 1967.
DOI : 10.4310/jdg/1214427880

F. Otto and C. Villani, Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality, Journal of Functional Analysis, vol.173, issue.2, pp.361-400, 2000.
DOI : 10.1006/jfan.1999.3557

]. S. She91 and . Sheu, Some estimates of the transition density of a nondegenerate diffusion Markov process Multidimensional diffusion processes, Ann. Probab, pp.19-21, 1979.

D. Talay and L. Tubaro, Expansion of the global error for numerical schemes solving stochastic differential equations, Stochastic Analysis and Applications, vol.20, issue.4, pp.8-494, 1990.
DOI : 10.1080/07362999008809220

URL : https://hal.archives-ouvertes.fr/inria-00075490