{"paper":{"title":"Convergence of a finite difference scheme to weak solutions of the system of partial differential equation arising in mean field games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"cs.NA","authors_text":"Alessio Porretta (DIPMAT), Yves Achdou (LJLL)","submitted_at":"2015-04-22T09:36:54Z","abstract_excerpt":"Mean field type models describing the limiting behavior of stochastic differential games as the number of players tends to +$\\infty$, 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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05705","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}