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

Cesaroni, Annalisa, Dirr, Nicolas ORCID: https://orcid.org/0000-0003-3634-7367 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:	28 Nov 2024 13:15
URI:	https://orca.cardiff.ac.uk/id/eprint/94101

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