{"title":"Monotone solutions for mean field games master equations: continuous state space and common noise","authors":"Charles Bertucci","doi":"10.1080/03605302.2023.2276564","DOIUrl":null,"url":null,"abstract":"AbstractWe present the notion of monotone solution of mean field games master equations in the case of a continuous state space. We establish the existence, uniqueness and stability of such solutions under standard assumptions. This notion allows us to work with solutions which are merely continuous in the measure argument, in the case of first order master equations. We study several structures of common noises, in particular ones in which common jumps (or aggregate shocks) can happen randomly, and ones in which the correlation of randomness is carried by an additional parameter.KEYWORDS: Mean Field GamesMaster equationWeak solutions Notes1 C−k is the topological dual set of C k while we understand C1,1 in the sense that the usual differential is a Lipschitz function.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"18","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Partial Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/03605302.2023.2276564","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 18
Abstract
AbstractWe present the notion of monotone solution of mean field games master equations in the case of a continuous state space. We establish the existence, uniqueness and stability of such solutions under standard assumptions. This notion allows us to work with solutions which are merely continuous in the measure argument, in the case of first order master equations. We study several structures of common noises, in particular ones in which common jumps (or aggregate shocks) can happen randomly, and ones in which the correlation of randomness is carried by an additional parameter.KEYWORDS: Mean Field GamesMaster equationWeak solutions Notes1 C−k is the topological dual set of C k while we understand C1,1 in the sense that the usual differential is a Lipschitz function.
期刊介绍：
This journal aims to publish high quality papers concerning any theoretical aspect of partial differential equations, as well as its applications to other areas of mathematics. Suitability of any paper is at the discretion of the editors. We seek to present the most significant advances in this central field to a wide readership which includes researchers and graduate students in mathematics and the more mathematical aspects of physics and engineering.
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