R. Alexandre, L. Desvillettes, C. Villani, and B. Wennberg, Entropy Dissipation and Long-Range Interactions, Archive for Rational Mechanics and Analysis, vol.152, issue.4, pp.327-355, 2000.
DOI : 10.1007/s002050000083

URL : http://www.cmla.ens-cachan.fr/Cmla/Publications/2000/CMLA2000-21.ps.gz

V. Bally and L. Caramellino, Convergence and regularity of probability laws by using an interpolation method, The Annals of Probability, vol.45, issue.2, pp.1110-1159, 2017.
DOI : 10.1214/15-AOP1082

URL : https://hal.archives-ouvertes.fr/hal-01109276

V. Bally, L. Caramellino, and R. Cont, Stochastic integration by parts and functional Itô calculus, Advanced Courses in Mathematics -CRM, 2016.
DOI : 10.1007/978-3-319-27128-6

V. Bally and E. Clement, Integration by parts formula and applications to equations with jumps, Probability Theory and Related Fields, vol.105, issue.4, pp.613-657, 2011.
DOI : 10.1007/BF01191910

URL : https://hal.archives-ouvertes.fr/hal-00431632

V. Bally and N. Fournier, Regularization properties of the 2D homogeneous Boltzmann equation without cutoff, Probability Theory and Related Fields, vol.15, issue.3, pp.659-704, 2011.
DOI : 10.4171/RMI/259

URL : https://hal.archives-ouvertes.fr/hal-00692754

C. Bennett and R. Sharpley, Interpolation of operators, 1988.

K. Bichteler, J. B. Gravereau, and J. Jacod, Malliavin calculus for processes with jumps. Gordon and Breach science publishers, 1987.

J. M. Bismut, Calcul des variations stochastique et processus de sauts, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.293, issue.2, pp.147-235, 1983.
DOI : 10.1515/crll.1931.164.27

N. Bouleau and L. Denis, Dirichlet forms and methods for Poisson point measures and Lévy processes. Probability Theory and Stochastic Modelling, p.76, 2015.
DOI : 10.1007/978-3-319-25820-1

A. Debussche and N. Fournier, Existence of densities for stable-like driven SDE??s with H??lder continuous coefficients, Journal of Functional Analysis, vol.264, issue.8, pp.1757-1778, 2013.
DOI : 10.1016/j.jfa.2013.01.009

A. Debussche and M. Romito, Existence of densities for the 3D Navier???Stokes equations driven by Gaussian noise, Probability Theory and Related Fields, vol.354, issue.6, pp.575-596, 2014.
DOI : 10.1007/978-3-0346-0419-2

URL : https://hal.archives-ouvertes.fr/hal-00676454

S. Marco, Smoothness and asymptotic estimates of densities for SDEs with locally smooth coefficients and applications to square root-type diffusions, The Annals of Applied Probability, vol.21, issue.4, pp.1282-1321, 2011.
DOI : 10.1214/10-AAP717

URL : https://hal.archives-ouvertes.fr/hal-00692982

N. Fournier, Existence and regularity study for 2D Bolzmann equation without cutoff by a probabilistic approach, Ann. Appl. Probab, vol.10, pp.434-462, 2000.

N. Fournier, Jumping SDE's: absolute continuity using monotonicity. Stochastic Process, Appl, vol.98, pp.317-330, 2002.
DOI : 10.1016/s0304-4149(01)00149-1

URL : https://doi.org/10.1016/s0304-4149(01)00149-1

N. Fournier, Smoothness of the law of some one-dimensional jumping S.D.E.s with non-constant rate of jump, Electronic Journal of Probability, vol.13, issue.0, pp.135-156, 2008.
DOI : 10.1214/EJP.v13-480

N. Fournier, Finiteness of entropy for the homogeneous Boltzmann equation with measure initial condition, The Annals of Applied Probability, vol.25, issue.2, pp.860-897, 2015.
DOI : 10.1214/14-AAP1012

URL : https://hal.archives-ouvertes.fr/hal-00731694

N. Fournier and C. Mouhot, On the Well-Posedness of the Spatially Homogeneous Boltzmann Equation with a Moderate Angular Singularity, Communications in Mathematical Physics, vol.3, issue.1-2, pp.803-824, 2009.
DOI : 10.1007/s10955-006-9208-6

URL : https://hal.archives-ouvertes.fr/hal-00135991

N. Fournier and J. Printems, Absolute continuity for some one-dimensional processes, Bernoulli, vol.16, issue.2, pp.343-360, 2010.
DOI : 10.3150/09-BEJ215

URL : https://hal.archives-ouvertes.fr/hal-00693025

I. M. Gamba, V. Panferov, and C. Villani, Upper Maxwellian Bounds for the Spatially Homogeneous Boltzmann Equation, Archive for Rational Mechanics and Analysis, vol.95, issue.1???2, pp.253-282, 2009.
DOI : 10.1023/A:1004546031908

URL : http://arxiv.org/pdf/math/0701081

C. Graham and . Meleard, Existence and Regularity of a Solution of a Kac Equation Without Cutoff Using the Stochastic Calculus of Variations, Communications in Mathematical Physics, vol.205, issue.3, pp.551-569, 1999.
DOI : 10.1007/s002200050689

H. Guerin, E. Meleard, and . Nualart, Exponential estimates for spatially homogeneous Landau equations via the Malliavin calculus, Journal of Func. Analysis, issue.2, pp.649-677, 2006.

Y. Ishikawa, Stochastic Calculus of variation for Jump Processes, De Gruyter Studies in Math, vol.54, 2013.
DOI : 10.1515/9783110282009

V. N. Kolokoltsov, On the regularity of the solutions of trhe space homogenuous Bolzmann equation with polynomial growing collision kernel. Advanced Studies in Contemporany Math, pp.9-38, 2006.

R. Leandre, Régularuté des processus de sauts gégénérés, Ann. Inst. H. Poincaré Probab. Statist, vol.21, pp.125-146, 1985.

E. Pardoux, B. Sentis, and . Lapeyre, Introduction to Monte-Carlo Methods for Transport and Diffusion Equations Oxford texts in applied and engineering mathematics, 2003.

H. Tanaka, Probabilistic treatment of the Boltzmann equation of Maxwellian molecules, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.47, issue.1, pp.67-105, 1978.
DOI : 10.1016/B978-1-4832-0022-4.50006-5