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A semi-discrete in time approximation for a model 1st order-finite horizon mean field game problem

Abstract : In this article we consider a model first order mean field game problem, introduced by J.M. Lasry and P.L. Lions in [17]. Its solution (v;m) can be obtained as the limit of the solutions of the second order mean field game problems, when the noise parameter tends to zero (see [17]). We propose a semi-discrete infitime approximation of the system and, under natural assumptions, we prove that it is well posed and that it converges to (v;m) when the discretization parameter tends to zero.
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Submitted on : Thursday, January 12, 2012 - 11:49:17 AM
Last modification on : Wednesday, November 3, 2021 - 2:18:08 PM
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Fabio Camilli, Francisco J. Silva. A semi-discrete in time approximation for a model 1st order-finite horizon mean field game problem. Networks and Heterogeneous Media, AIMS-American Institute of Mathematical Sciences, 2012, 7 (2), pp.263 - 277. ⟨10.3934/nhm.2012.7.263⟩. ⟨hal-00659171⟩

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