Uniform propagation of chaos for a class of nonlinear diffusions

Pierre del Moral (1, 2) , Julian Tugaut (3)

1 ALEA - Advanced Learning Evolutionary Algorithms
2 IMB - Institut de Mathématiques de Bordeaux
3 ICJ - Institut Camille Jordan

We are interested in nonlinear diffusions in which the own law intervenes in the drift. This kind of diffusions corresponds to the hydrodynamical limit of some particle system. One also talks about propagation of chaos. It is well known, for McKean-Vlasov diffusions, that such a propagation of chaos holds on finite time interval. However, it has been proved that the lack of convexity of the external force implies that there is no uniform propagation of chaos if the diffusion coefficient is small enough. We here aim to establish a uniform propagation of chaos even if the external force is not convex, with a diffusion coefficient sufficiently large. The idea consists in combining the propagation of chaos on a finite time interval with a functional inequality, already used by Bolley, Gentil and Guillin.

Mots clés: Nonlinear diffusions; Propagation of chaos; Feynman-Kac; McKean-Vlasov models; Functional inequality

Domaines: Probabilités [math.PR]

Pierre del Moral, Julian Tugaut. Uniform propagation of chaos for a class of nonlinear diffusions. 2013. ⟨hal-00798813v2⟩