In this article we consider a model first order mean field game problem, introduced by J.M. Lasry and P.L. Lions in [18]. 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 [18]). We propose a semi-discrete in time 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. © American Institute of Mathematical Sciences.

A semi-discrete approximation for a first order mean field game problem / Camilli, Fabio; Francisco, Silva. - In: NETWORKS AND HETEROGENEOUS MEDIA. - ISSN 1556-1801. - STAMPA. - 7:2(2012), pp. 263-277. [10.3934/nhm.2012.7.263]

A semi-discrete approximation for a first order mean field game problem

CAMILLI, FABIO;
2012

Abstract

In this article we consider a model first order mean field game problem, introduced by J.M. Lasry and P.L. Lions in [18]. 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 [18]). We propose a semi-discrete in time 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. © American Institute of Mathematical Sciences.
convex duality; mean eld games; optimal control; mean field games; numerical methods
01 Pubblicazione su rivista::01a Articolo in rivista
A semi-discrete approximation for a first order mean field game problem / Camilli, Fabio; Francisco, Silva. - In: NETWORKS AND HETEROGENEOUS MEDIA. - ISSN 1556-1801. - STAMPA. - 7:2(2012), pp. 263-277. [10.3934/nhm.2012.7.263]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/454949
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