ABSTRACT
In this chapter, the authors study the non-linear diffusion processes, introduced in the 1960s by McKean, and tackle their simulation: processes of this type correspond to stochastic differential equations in which the distribution of the diffusion process is itself an unknown of the equation; talk about non-linear diffusions in the McKean sense. They give several illustrations of the interacting particle phenomena. The aggregation phenomena in the populations or social networks offer a natural setting for interaction models. The author also shows that each stochastic differential equation of the particles system converges to the stochastic differential equation where the empirical measure is replaced by the distribution of the process. This is the passage from the microscopic scale to the macroscopic scale mentioned at the beginning, where one particle in a much populated environment approximately behaves like in a mean-field interaction (due to the normalization with the factor 1/N in the equations).
