References
- F.Bolley, A.Guillin, and C.Villani, Quantitative concentration inequalities for empirical measures on non-compact spaces, Probab. Theory Relat. Fields137(3–4) (2007), pp. 541–593.
- S.Benachour, B.Roynette, D.Talay, and P.Vallois, Nonlinear self-stabilizing processes. I. Existence, invariant probability, propagation of chaos, Stochastic Process. Appl.75(2) (1998), pp. 173–201.
- S.Benachour, B.Roynette, and P.Vallois, Nonlinear self-stabilizing processes. II. Convergence to invariant probability, Stochastic Process. Appl.75(2) (1998), pp. 203–224.
- P.Cattiaux, A.Guillin, and F.Malrieu, Probabilistic approach for granular media equations in the non-uniformly convex case, Probab. Theory Relat. Fields140(1–2) (2008), pp. 19–40.
- J.A.Carrillo, R.J.McCann, and C.Villani, Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates, Rev. Mat. Iberoamericana19(3) (2003), pp. 971–1018.
- D.A.Dawson and J.Gärtner, Large deviations from the McKean-Vlasov limit for weakly interacting diffusions, Stochastics20(4) (1987), pp. 247–308.
- T.Funaki, A certain class of diffusion processes associated with nonlinear parabolic equations, Z. Wahrsch. Verw. Gebiete67(3) (1984), pp. 331–348.
- S.Herrmann, P.Imkeller, and D.Peithmann, Large deviations and a Kramers' type law for self-stabilizing diffusions, Ann. Appl. Probab.18(4) (2008), pp. 1379–1423.
- S.Herrmann and J.Tugaut, Self-stabilizing processes: uniqueness problem for stationary measures and convergence rate in the small noise limit, ESAIM P&S. (2009). Available at http://hal.archives-ouvertes.fr/hal-00599139/fr/.
- S.Herrmann and J.Tugaut, Non-uniqueness of invariant probabilities for self-stabilizing processes, Stochastic Process. Appl.120(7) (2010), pp. 1215–1246.
- S.Herrmann and J.Tugaut, Stationary measures for self-stabilizing processes: Asymptotic analysis in the small noise limit, Electron. J. Probab.15 (2010), pp. 2087–2116.
- F.Malrieu, Logarithmic Sobolev inequalities for some nonlinear PDE's, Stochastic Process. Appl.95(1) (2001), pp. 109–132.
- F.Malrieu, Convergence to equilibrium for granular media equations and their Euler schemes, Ann. Appl. Probab.13(2) (2003), pp. 540–560.
- H.P.McKean, Jr, Propagation of Chaos for a Class of Non-linear Parabolic Equations, in Stochastic Differential Equations (Lecture Series in Differential Equations, Session 7, Catholic University, 1967), Air Force Office Scientific Research, Arlington, VA, 1967, pp. 41–57.
- S.Méléard, Asymptotic Behaviour of Some Interacting Particle Systems; McKean–Vlasov and Boltzmann Models, in Probabilistic Models for Nonlinear Partial Differential Equations (Montecatini Terme, 1995), Vol. 1627 of Lecture Notes in Mathematics, Springer, Berlin, 1996, pp. 42–95.
- A.-S.Sznitman, Topics in Propagation of Chaos, in École d'Été de Probabilités de Saint-Flour XIX–1989, Vol. 1464 of Lecture Notes in Mathematics, Springer, Berlin, 1991, pp. 165–251.
- Y.Tamura, On asymptotic behaviors of the solution of a nonlinear diffusion equation, J. Fac. Sci. Univ. Tokyo Sect. IA Math.31(1) (1984), pp. 195–221.
- Y.Tamura, Free energy and the convergence of distributions of diffusion processes of McKean type, J. Fac. Sci. Univ. Tokyo Sect. IA Math.34(2) (1987), pp. 443–484.
- J.Tugaut, Convergence to the equilibria for self-stabilizing processes in double well landscape, Ann. Probab. (2010). Available at http://hal.archives-ouvertes.fr/hal-00573045/fr/.
- J.Tugaut, Self-stabilizing processes in multi-wells landscape in – Invariant probabilities, J. Theor. Probab. (2011). Available at http://hal.archives-ouvertes.fr/hal-00627901/fr/.
- A.Y.Veretennikov, On Ergodic Measures for McKean–Vlasov Stochastic Equations, In Monte Carlo and Quasi-Monte Carlo Methods 2004, Springer, Berlin, 2006.