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;
2012-01-01
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.File in questo prodotto:
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