平均场游戏与共同的噪音

IF 2.1 1区数学 Q1 STATISTICS & PROBABILITY

Annals of Probability Pub Date : 2014-07-23 DOI:10.1214/15-AOP1060

R. Carmona, F. Delarue, D. Lacker

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引用次数: 208

摘要

建立了具有共同噪声的一般随机微分平均场对策的存在唯一性理论。与随机微分方程理论类比，引入了强解和弱解的概念，并在非常一般的假设下证明了平均场对策的弱解的存在性。举例和反例是为了启发存在理论的基础。最后，给出了Yamada和Watanabe著名结果的一个类比，并证明了在附加假设下强解的存在唯一性。

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Mean field games with common noise

A theory of existence and uniqueness is developed for general stochastic differential mean field games with common noise. The concepts of strong and weak solutions are introduced in analogy with the theory of stochastic differential equations, and existence of weak solutions for mean field games is shown to hold under very general assumptions. Examples and counter-examples are provided to enlighten the underpinnings of the existence theory. Finally, an analog of the famous result of Yamada and Watanabe is derived, and it is used to prove existence and uniqueness of a strong solution under additional assumptions.

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来源期刊

Annals of Probability 数学-统计学与概率论

CiteScore

4.60

自引率

8.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Annals of Probability publishes research papers in modern probability theory, its relations to other areas of mathematics, and its applications in the physical and biological sciences. Emphasis is on importance, interest, and originality – formal novelty and correctness are not sufficient for publication. The Annals will also publish authoritative review papers and surveys of areas in vigorous development.