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

Mean field-type models describing the limiting behavior of stochastic differential games as the number of players tends to +∞ 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...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 2016-01, Vol.54 (1), p.161-186
Main Authors: ACHDOU, YVES, PORRETTA, ALESSIO
Format: Article
Language:English
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Summary:Mean field-type models describing the limiting behavior of stochastic differential games as the number of players tends to +∞ 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.
ISSN:0036-1429
1095-7170
DOI:10.1137/15M1015455