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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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Published in: | SIAM journal on numerical analysis 2016-01, Vol.54 (1), p.161-186 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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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. |
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ISSN: | 0036-1429 1095-7170 |
DOI: | 10.1137/15M1015455 |