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arXiv 1503.07754math.OCmath.APmath.PR
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关于主方程的解释

On The Interpretation Of The Master Equation

Alain Bensoussan, Jens Frehse, Phillip Yam

摘要:

自P.L.狮子在他的讲座和研讨会在法兰西学院,见[9],也是非常有益的注意Cardialaguet [4]对狮子的讲座,主方程吸引了很多的兴趣,并提出了各种观点,例如见Carmona-Delarue [5],Bensoussan-Frehse-Yam [2],Buckdahn-Li-Peng-Rainer [3]。有几种方法来引入这种类型的方程;在那些提到的作品中,它们涉及一个参数,这是一个概率测度,而P. L. Lions最近提出了用希尔伯特空间中的平方可积〔的〕随机变量工作的思想。因此,写方程是一个问题;而另一个问题是它的起源。在这篇文章中,我们讨论了所有这些不同的方面,我们的建模论点在很大程度上依赖于法国学院由P.L.狮子座2014年11月14日

英文摘要:

Since its introduction by P.L. Lions in his lectures and seminars at the College de France, see [9], and also the very helpful notes of Cardialaguet [4] on Lions' lectures, the Master Equation has attracted a lot of interest, and various points of view have been expressed, see for example Carmona-Delarue [5], Bensoussan-Frehse-Yam [2], Buckdahn-Li-Peng-Rainer [3]. There are several ways to introduce this type of equation; and in those mentioned works, they involve an argument which is a probability measure, while P.L. Lions has recently proposed the idea of working with the Hilbert space of square integrable random variables. Hence writing the equation is an issue; while another issue is its origin. In this article, we discuss all these various aspects, and our modeling argument relies heavily on a seminar at College de France delivered by P.L. Lions on November 14, 2014.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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