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Convergence of the solutions of the MFG discounted Hamilton-Jacobi equation

Masoero, Marco (2019-06), Convergence of the solutions of the MFG discounted Hamilton-Jacobi equation. https://basepub.dauphine.fr/handle/123456789/19407

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1906.01505.pdf (198.8Kb)
Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-02148470
Date
2019-06
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Published in
Paris
Pages
17
Metadata
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Author(s)
Masoero, Marco
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We consider the solution Vδ of the discounted Hamilton-Jacobi equation in the Wasserstein space arising from potential MFG and we prove its full convergence to a corrector function χ0. We follow the structure of the proof of the analogue result in the finite dimensional setting provided by Davini, Fathi, Iturriaga, Zavidovique in 2017. We characterize the limit χ0 through a particular set of smooth Mather measures. A major point that distinguishes the techniques deployed in the standard setting from the ones that we use here is the lack of mollification in the Wasserstain space.
Subjects / Keywords
amilton-Jacobi equation; Wasserstein space; MFG

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