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Homogenization of a mean field game system in the small noise limit

Cesaroni, Annalisa, Dirr, Nicolas and Marchi, Claudio 2016. Homogenization of a mean field game system in the small noise limit. SIAM Journal on Mathematical Analysis 48 (4) , pp. 2701-2729. 10.1137/16M1063459

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Abstract

This paper concerns the simultaneous effect of homogenization and of the small noise limit for a second order mean field game (MFG) system with local coupling and quadratic Hamiltonian. We show under some additional assumptions that the solutions of our system converge to a solution of an effective first order system whose effective operators are defined through a cell problem which is a second order system of ergodic MFG type. We provide several properties of the effective operators, and we show that in general the effective system loses the MFG structure.

Item Type: Article
Date Type: Published Online
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Additional Information: Published PDF uploaded in accordance with policy at http://www.sherpa.ac.uk/romeo/issn/0036-1410/ [Accessed 01/09/2016]
Publisher: Society for Industrial and Applied Mathematics
ISSN: 0036-1410
Funders: EPSRC, Leverhulme
Date of First Compliant Deposit: 31 August 2016
Date of Acceptance: 6 June 2016
Last Modified: 25 Feb 2020 12:00
URI: http://orca.cf.ac.uk/id/eprint/94101

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