On Fully Nonlinear Parabolic Mean Field Games with Nonlocal and Local Diffusions

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-09-12 DOI:10.1137/23m1615528

Indranil Chowdhury, Espen R. Jakobsen, Miłosz Krupski

引用次数: 0

Abstract

SIAM Journal on Mathematical Analysis, Volume 56, Issue 5, Page 6302-6336, October 2024.
Abstract. We introduce a class of fully nonlinear mean field games posed in [math]. We justify that they are related to controlled local or nonlocal diffusions, and more generally in our setting, to a new control interpretation involving time change rates of stochastic (Lévy) processes. The main results are the existence and uniqueness of solutions under general assumptions. These results are applied to nondegenerate equations—including both local second-order and nonlocal with fractional Laplacians. Uniqueness holds under the monotonicity of couplings and convexity of the Hamiltonian, but neither monotonicity nor convexity need to be strict. We consider a rich class of nonlocal operators and processes and develop tools to work in the whole space without explicit moment assumptions.

查看原文本刊更多论文

论具有非局部和局部扩散的完全非线性抛物平均场博弈

SIAM 数学分析期刊》，第 56 卷，第 5 期，第 6302-6336 页，2024 年 10 月。摘要。我们介绍了[math]中提出的一类全非线性均场博弈。我们证明，它们与受控局部或非局部扩散相关，在我们的环境中，与涉及随机（Lévy）过程时间变化率的新控制解释相关。主要结果是一般假设条件下解的存在性和唯一性。这些结果适用于非enerate方程，包括局部二阶和非局部分数拉普拉斯方程。唯一性在耦合的单调性和哈密顿的凸性条件下成立，但单调性和凸性都不必严格。我们考虑了丰富的非局部算子和过程，并开发了在整个空间中工作而无需明确时刻假设的工具。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.