Mean field type models describing the limiting behavior of stochastic
differential games as the number of players tends to +∞, have been
recently introduced by J-M. Lasry and P-L. Lions. Under suitable assumptions,
they lead to a system of two coupled partial differential equations, a forward
Bellman equation and a backward Fokker-Planck equations. Finite difference
schemes for the approximation of such systems have been proposed in previous
works. Here, we prove the convergence of these schemes towards a weak solution
of the system of partial differential equations