Mean field-type models describing the limiting behavior of stochastic differential games as the number of players tends to +infinity were recently introduced by Lasry and Lions. Under suitable assumptions, they lead to a system of two coupled partial differential equations, a forward Bellman equation and a backward Fokker-Planck equation. 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.
Achdou, Y., Porretta, A. (2016). Convergence of a finite difference scheme to weak solutions of the system of partial differential equations arising in mean field games. SIAM JOURNAL ON NUMERICAL ANALYSIS, 54(1), 161-186 [10.1137/15M1015455].
Convergence of a finite difference scheme to weak solutions of the system of partial differential equations arising in mean field games
PORRETTA, ALESSIO
2016-01-01
Abstract
Mean field-type models describing the limiting behavior of stochastic differential games as the number of players tends to +infinity were recently introduced by Lasry and Lions. Under suitable assumptions, they lead to a system of two coupled partial differential equations, a forward Bellman equation and a backward Fokker-Planck equation. 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.File | Dimensione | Formato | |
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