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Convergence of a finite difference scheme to weak solutions of the system of partial differential equation arising in mean field games

机译:均值博弈中偏微分方程组弱解的有限差分格式的收敛性

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摘要

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.
机译:J-M最近引入了描述随玩家数量趋于+∞的随机差分游戏的限制行为的平均场类型模型。 Lasry和P-L。狮子在适当的假设下,它们导致一个由两个耦合的偏微分方程组组成的系统,一个正向的Bellman方程和一个反向的Fokker-Planck方程。在以前的工作中已经提出了用于近似这种系统的有限差分方案。在这里,我们证明了这些方案对于偏微分方程组的弱解的收敛性。

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