WELL-POSEDNESS OF MEAN FIELD GAMES MASTER EQUATIONS INVOLVING NON-SEPARABLE LOCAL HAMILTONIANS

David M. Ambrose, Alpár R. Mészáros

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In this paper we construct short time classical solutions to a class of master equations in the presence of non-degenerate individual noise arising in the theory of mean field games. The considered Hamiltonians are non-separable and local functions of the measure variable, therefore the equation is restricted to absolutely continuous measures whose densities lie in suitable Sobolev spaces. Our results hold for smooth enough Hamiltonians, without any additional structural conditions as convexity or monotonicity.
Original languageEnglish (US)
Pages (from-to)2481-2523
Number of pages43
JournalTransactions of the American Mathematical Society
Volume376
Issue number4
DOIs
StatePublished - Jan 24 2023
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics

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