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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.