Open AccessA semi-discrete approximation for a first order mean field game problem
Author(s) -
Fabio Camilli,
F.J.G. Silva
Publication year - 2012
Publication title -
networks and heterogeneous media
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.732
H-Index - 34
eISSN - 1556-181X
pISSN - 1556-1801
DOI - 10.3934/nhm.2012.7.263
Subject(s) - discretization , zero (linguistics) , limit (mathematics) , mathematics , mean field theory , order (exchange) , field (mathematics) , zero order , mathematical analysis , first order , physics , pure mathematics , quantum mechanics , philosophy , linguistics , finance , economics
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
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