M. Arnaudon, A. Thalmaier, and F. Wang, Gradient estimates and Harnack inequalities on non-compact Riemannian manifolds, Stochastic Process, Appl, vol.119, issue.10, pp.3653-3670, 2009.

V. Barbu, M. Röckner, and F. Russo, Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case, Probability Theory and Related Fields, vol.34, issue.6, pp.1-43, 2011.
DOI : 10.1007/s00440-010-0291-x

URL : https://hal.archives-ouvertes.fr/inria-00410248

G. I. Barenblatt, On some unsteady motions of a liquid and gas in a porous medium, Akad. Nauk SSSR. Prikl. Mat. Meh, vol.16, pp.67-78, 1952.

N. Belaribi, F. Cuvelier, and F. Russo, A probabilistic algorithm approximating solutions of a singular PDE of porous media type, Monte Carlo Methods and Applications, vol.17, issue.4, pp.317-369, 2011.
DOI : 10.1515/mcma.2011.014

URL : https://hal.archives-ouvertes.fr/inria-00535806

S. Benachour, P. Chassaing, B. Roynette, and P. Vallois, Processus associés à l'équation des milieux poreux, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.23, issue.4 4, pp.793-832, 1996.

P. Benilan and M. G. Crandall, The continuous dependence on ? of solutions of ut ???(u) = 0, Math. J, vol.30, issue.2, pp.161-177, 1981.

P. Blanchard, M. Röckner, and F. Russo, Probabilistic representation for solutions of an irregular porous media type equation, The Annals of Probability, vol.38, issue.5, pp.1870-1900, 2010.
DOI : 10.1214/10-AOP526

URL : https://hal.archives-ouvertes.fr/hal-00279975

V. I. Bogachev, G. Da-prato, and M. Röckner, Infinite dimensional Kolmogorov operators with time dependent drift coefficients, Doklady Mathematics, vol.77, issue.2, pp.587-591, 2008.
DOI : 10.1134/S1064562408020294

V. I. Bogachev, G. Da-prato, M. Röckner, and W. Stannat, Uniqueness of solutions to weak parabolic equations for measures, Bulletin of the London Mathematical Society, vol.39, issue.4, pp.631-640, 2007.
DOI : 10.1112/blms/bdm046

H. Brezis and M. G. Crandall, Uniqueness of solutions of the initial-value problem for ut ? ??(u) = 0, J. Math. Pures Appl, vol.58, issue.9 2, pp.153-163, 1979.

H. Brezis and A. Friedman, Non linear parabolic equations involving measures as initial conditions, J. Math. Pures Appl, vol.62, issue.9 1, pp.73-97, 1983.

F. Cavalli, G. Naldi, G. Puppo, and M. Semplice, High-Order Relaxation Schemes for Nonlinear Degenerate Diffusion Problems, SIAM Journal on Numerical Analysis, vol.45, issue.5, pp.2098-2119, 2007.
DOI : 10.1137/060664872

E. Chasseigne and J. L. Vazquez, Theory of Extended Solutions??for Fast-Diffusion Equations??in Optimal Classes of Data.??Radiation from Singularities, Archive for Rational Mechanics and Analysis, vol.164, issue.2, pp.133-187, 2002.
DOI : 10.1007/s00205-002-0210-0

J. Dolbeault and G. Toscani, Fast diffusion equations: Matching large time asymptotics by relative entropy methods, Kinetic and Related Models, vol.4, issue.3, pp.701-716, 2011.
DOI : 10.3934/krm.2011.4.701

URL : https://hal.archives-ouvertes.fr/hal-00482898

A. Figalli, Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients, Journal of Functional Analysis, vol.254, issue.1, pp.109-153, 2008.
DOI : 10.1016/j.jfa.2007.09.020

A. Figalli and R. Philipowski, Convergence to the viscous porous medium equation and propagation of chaos, ALEA Lat, Am. J. Probab. Math. Stat, vol.4, pp.185-203, 2008.

C. Graham, T. G. Kurtz, S. Méléard, S. Ph, M. Protter et al., Probabilistic models for nonlinear partial differential equations, Lectures given at the 1st Session and Summer School held in Montecatini Terme, Lecture Notes in Mathematics, pp.22-30, 1995.

M. A. Herrero and M. Pierre, The Cauchy problem for ut = ?u m when 0 < m < 1

F. Hirsch, C. Profeta, B. Roynette, and M. Yor, Peacocks and associated martingales, with explicit constructions, 2011.
DOI : 10.1007/978-88-470-1908-9

URL : https://hal.archives-ouvertes.fr/hal-00657769

J. Jacod, Theoremes Limite Pour Les Processus, Lecture Notes in Math, vol.1117, pp.298-409, 1985.
DOI : 10.1007/BFb0099423

I. Karatzas and S. E. Shreve, Brownian motion and stochastic calculus, Graduate Texts in Mathematics, vol.113, 1991.
DOI : 10.1007/978-1-4612-0949-2

T. Lukkari, The fast diffusion equation with measure data, Nonlinear Differential Equations and Applications NoDEA, vol.146, issue.12, pp.329-6343, 2012.
DOI : 10.1007/s00030-011-0131-4

P. Malliavin, Stochastic analysis, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of, Mathematical Sciences], vol.313, 1997.

S. Marco, On probability distributions of diffusions and financial models with non-globally smooth coefficients, 2010.
URL : https://hal.archives-ouvertes.fr/tel-00588686

H. P. Jr and . Mckean, Propagation of chaos for a class of non-linear parabolic equations., Stochastic Differential Equations (Lecture Series in Differential Equations, Session 7, Catholic Univ, Air Force Office Sci. Res, pp.41-57, 1967.

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

R. Philipowski, Interacting diffusions approximating the porous medium equation and propagation of chaos, Stochastic Process, Appl, vol.117, issue.4, pp.526-538, 2007.

M. Pierre, Nonlinear fast diffusion with measures as data, Pitman Res. Notes Math. Ser, vol.149, pp.179-188, 1987.

M. Röckner and X. Zhang, Weak uniqueness of Fokker???Planck equations with degenerate and bounded coefficients, Comptes Rendus Mathematique, vol.348, issue.7-8, pp.435-438, 2010.
DOI : 10.1016/j.crma.2010.01.001

E. M. Stein, Singular integrals and estimates for the Cauchy-Riemann equations, Bulletin of the American Mathematical Society, vol.79, issue.2, pp.79-440, 1973.
DOI : 10.1090/S0002-9904-1973-13205-7

D. W. Stroock and S. R. Varadhan, Multidimensional diffusion processes, Classics in Mathematics, 2006.
DOI : 10.1007/3-540-28999-2

A. S. Sznitman, Topics in propagation of chaos, Lecture Notes in Math, vol.22, issue.1, pp.165-251, 1991.
DOI : 10.1070/SM1974v022n01ABEH001689

J. L. Vazquez, The porous medium equation, 2007.
DOI : 10.1093/acprof:oso/9780198569039.001.0001