V. Bally and L. Caramellino, Asymptotic development for the CLT in total variation distance, Bernoulli, vol.22, issue.4, pp.2442-2485, 2016.
DOI : 10.3150/15-BEJ734
URL : https://hal.archives-ouvertes.fr/hal-01104866

V. Bally and L. Caramellino, On the distances between probability density functions, Electronic Journal of Probability, vol.19, issue.0, pp.1-33, 2014.
DOI : 10.1214/EJP.v19-3175

V. Bally and L. Caramellino, An invariance principle for stochastic series I. Gaussian limits, 2015.

V. Bally and E. Clément, Integration by parts formula and applications to equations with jumps. Probab. Theory Related Fields, pp.613-657, 2011.
DOI : 10.1007/s00440-010-0310-y
URL : https://hal.archives-ouvertes.fr/hal-00431632

D. Bakry, I. Gentil, and M. , Ledoux Analysis and Geometry of Markov Diffusion Semigroups, 2014.
DOI : 10.1007/978-3-319-00227-9

V. Bentkus, On Hoeffding?s inequalities, The Annals of Probability, vol.32, issue.2, pp.1650-1673, 2004.
DOI : 10.1214/009117904000000360

K. Bichtler, J. Gravereaux, and J. Jacod, Malliavin calculus for processes with jumps, 1987.

A. Carbery and J. Wright, Distributional and $L^{q}$ norm inequalities for polynomials over convex bodies in ${\Bbb R}^n$, Mathematical Research Letters, vol.8, issue.3, pp.233-248, 2001.
DOI : 10.4310/MRL.2001.v8.n3.a1

P. De and J. , A central limit theorem for generalized quadratic forms, Probab. Th. Rel. Fields, vol.75, pp.261-277, 1987.

P. De and J. , A central limit theorem for generalized multilinear forms, Journal of Multivariate Analysis, vol.34, pp.275-289, 1990.

R. A. Fisher, Moments and Product Moments of Sampling Distributions, Proceedings of the London Mathematical Society, pp.199-238, 1929.
DOI : 10.1112/plms/s2-30.1.199

W. Hoeffding, A Class of Statistics with Asymptotically Normal Distribution, The Annals of Mathematical Statistics, vol.19, issue.3, pp.293-325, 1948.
DOI : 10.1214/aoms/1177730196

N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion processes. North- Holland Mathematical Library 24, 1989.

R. Latala, Estimates of moments and tails of Gaussian chaoses, The Annals of Probability, vol.34, issue.6, pp.2315-2331, 2006.
DOI : 10.1214/009117906000000421

A. J. Lee, U-Statistics: Theory and Practice, 1990.

D. Malicet and G. Poly, Properties of convergence in Dirichlet structures, Journal of Functional Analysis, vol.264, issue.9, pp.2077-2096, 2013.
DOI : 10.1016/j.jfa.2013.02.007
URL : https://hal.archives-ouvertes.fr/hal-00691126

E. Mossel, R. O. Donnell, and K. Oleszkiewicz, Noise stability of functions with low influences: Invariance and optimality, Annals of Mathematics, vol.171, issue.1, pp.295-341, 2010.
DOI : 10.4007/annals.2010.171.295

S. Noreddine and I. Nourdin, On the Gaussian approximation of vector-valued multiple integrals, Journal of Multivariate Analysis, vol.102, issue.6, pp.1008-1017, 2011.
DOI : 10.1016/j.jmva.2011.02.001
URL : https://hal.archives-ouvertes.fr/hal-00720353

I. Nourdin and G. Peccati, Normal Approximations Using Malliavin Calculus: from Stein's Method to Universality, Cambridge Tracts in Mathematics, 2012.

I. Nourdin and G. Peccati, Stein???s method on Wiener chaos, Probability Theory and Related Fields, vol.25, issue.4, pp.75-118, 2009.
DOI : 10.1007/s00440-008-0162-x

I. Nourdin, G. Peccati, and G. Reinert, Invariance principles for homogeneous sums: Universality of Gaussian Wiener chaos, The Annals of Probability, vol.38, issue.5, 1947.
DOI : 10.1214/10-AOP531
URL : https://hal.archives-ouvertes.fr/hal-00523525

I. Nourdin, G. Peccati, and A. Réveillac, Multivariate normal approximation using Stein???s method and Malliavin calculus, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.46, issue.1, pp.45-58, 2010.
DOI : 10.1214/08-AIHP308
URL : http://arxiv.org/abs/0804.1889

I. Nourdin and G. Poly, Convergence in total variation on Wiener chaos. Stochastic Process, Appl, vol.123, pp.651-674, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00696499

I. Nourdin and G. Poly, Convergence in law in the second Wiener/Wigner chaos. Convergence in law in the second Wiener/Wigner chaos, Elect. Comm. in Probab, vol.17, issue.36, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00696501

D. Nualart, The Malliavin calculus and related topics. Second Edition, 2006.
DOI : 10.1007/978-1-4757-2437-0

D. Nualart and S. Ortiz-latorre, Central limit theorems for multiple stochastic integrals and Malliavin calculus, Stochastic Processes and their Applications, vol.118, issue.4, pp.614-628, 2008.
DOI : 10.1016/j.spa.2007.05.004
URL : http://doi.org/10.1016/j.spa.2007.05.004

D. Nualart and G. Peccati, Central limit theorems for sequences of multiple stochastic integrals, The Annals of Probability, vol.33, issue.1, pp.177-193, 2005.
DOI : 10.1214/009117904000000621

G. Peccati and C. A. Tudor, Gaussian Limits for Vector-valued Multiple Stochastic Integrals, pp.247-262, 2004.
DOI : 10.1007/978-3-540-31449-3_17

Y. V. Prohorov, A local theorem for densities. Doklady Akad, Nauk SSSR (N.S.), vol.83, pp.797-800, 1952.

B. A. Sevastianov, The class of limit laws for distributions of quadratic forms in normal variables, Theor. Probability Appl, vol.6, pp.368-372, 1961.