平均场博弈主方程的单调解:连续状态空间和共噪声

IF 2.1 2区数学 Q1 MATHEMATICS

Communications in Partial Differential Equations Pub Date : 2023-11-08 DOI:10.1080/03605302.2023.2276564

Charles Bertucci

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引用次数: 18

摘要

摘要给出了连续状态空间下平均场博弈主方程单调解的概念。在标准假设下，建立了这类解的存在唯一性和稳定性。这个概念允许我们在一阶主方程的情况下，处理在测度参数中仅仅是连续的解。我们研究了几种常见噪声的结构，特别是那些可以随机发生共同跳跃(或集合冲击)的结构，以及那些随机相关性由附加参数携带的结构。注1 C−k是C k的拓扑对偶集，而我们在通常的微分是Lipschitz函数的意义上理解C1,1。

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Monotone solutions for mean field games master equations: continuous state space and common noise

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.

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来源期刊

Communications in Partial Differential Equations 数学-数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

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.