A Quadratic Mean Field Games Model for the Langevin Equation

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 19 Apr 2021Embargo end date: 01 Jul 2020 Italy English Publisher:MDPI AGJournal:Axioms, volume 10, page 68 (eissn: 2075-1680,

Copyright policy )

Authors: Camilli F.;

doi: 10.3390/axioms10020068 , 10.48550/arxiv.2007.10620

arXiv: 2007.10620

handle: 11564/843569 , 11573/1566710

A Quadratic Mean Field Games Model for the Langevin Equation

- Summary
- Subjects
- Metrics

Abstract

We consider a Mean Field Games model where the dynamics of the agents is given by a controlled Langevin equation and the cost is quadratic. An appropriate change of variables transforms the Mean Field Games system into a system of two coupled kinetic Fokker–Planck equations. We prove an existence result for the latter system, obtaining consequently existence of a solution for the Mean Field Games system.

Country

Italy

Related Organizations

Keywords

35K40, 91A13, Algebra and Number Theory, hypoel-liptic operators; kinetic Fokker–Planck equation; Langevin equation; mean field games system, hypoelliptic operators, Mean Field Games system, Mathematics - Analysis of PDEs, Optimization and Control (math.OC), langevin equation, QA1-939, FOS: Mathematics, Computer Science and Mathematics, Mathematics - Optimization and Control, Mathematics, kinetic Fokker–Planck equation, Analysis of PDEs (math.AP)

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	3
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Top 10%
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average