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Mean Field Games: Convergence of a Finite Difference Method

Abstract : 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. Numerical methods for the approximation of the stationary and evolutive versions of such models have been proposed by the authors in previous works. Here, convergence theorems for these methods are proved under various assumptions on the coupling operator.
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Yves Achdou, Fabio Camilli, Italo Capuzzo-Dolcetta. Mean Field Games: Convergence of a Finite Difference Method. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2013, 51 (5), pp.2585 - 2612. ⟨10.1137/120882421⟩. ⟨hal-01456506⟩

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