确定性平均场博弈中的降维技术

IF 2.1 2区数学 Q1 MATHEMATICS

Communications in Partial Differential Equations Pub Date : 2021-05-06 DOI:10.1080/03605302.2021.1998911

J. Lasry, P. Lions, B. Seeger

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引用次数: 6

摘要

摘要我们给出了平均场对策理论中产生的方程的例子，这些方程可以简化为更小维度的系统。这样的例子出现在某些应用中，它们可以用作建模工具来数值逼近更复杂的问题。在有限状态空间和无限状态空间两种情况下，都给出了导致归约现象的一般条件。我们还比较了带有噪声的方程的解及其在小噪声展开中的简化版本。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Dimension reduction techniques in deterministic mean field games

Abstract We present examples of equations arising in the theory of mean field games that can be reduced to a system in smaller dimensions. Such examples come up in certain applications, and they can be used as modeling tools to numerically approximate more complicated problems. General conditions that bring about reduction phenomena are presented in both the finite and infinite state-space cases. We also compare solutions of equations with noise with their reduced versions in a small-noise expansion.

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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.