CONVERGENCE OF A FINITE DIFFERENCE SCHEME TO WEAK SOLUTIONS OF THE SYSTEM OF PARTIAL DIFFERENTIAL EQUATIONS ARISING IN MEAN FIELD GAMES

被引：34

作者：

Achdou, Yves ^{[1
]}

Porretta, Alessio ^{[2
]}

机构：

[1] Univ Paris Diderot, CNRS, UPMC, Lab Jacques Louis Lions,UMR 7598,Sorbonne Paris C, F-75205 Paris, France

[2] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2016年 / 54卷 / 01期

关键词：

mean field games; weak solutions; finite difference schemes; convergence; SEMI-LAGRANGIAN SCHEME; NONLINEAR DIFFUSION; NUMERICAL-METHODS;

D O I：

10.1137/15M1015455

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：161 / 186

页数：26

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