平均场型二次BSDEs

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2023-01-01 DOI:10.3934/naco.2022009

Hélène Hibon, Ying Hu, Shanjian Tang

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引用次数: 3

摘要

本文给出了二次型BSDE的可解性的几个新结果，该方程的生成器也依赖于两个变量的均值。首先，我们使用BMO鞅的John-Nirenberg不等式来考虑这样的BSDE，以估计其对第一个未知变量的演化的贡献。然后，我们考虑BSDE除了通常的二次生成器之外，还具有二次生成器的附加期望值。在这种情况下，当通常的二次生成器既不依赖于第一个变量也不依赖于它的平均值时，我们对第一个未知变量使用确定性移位变换。一般情况可以用不动点论证来处理。

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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Mean-field type quadratic BSDEs

In this paper, we give several new results on solvability of a quadratic BSDE whose generator depends also on the mean of both variables. First, we consider such a BSDE using John-Nirenberg's inequality for BMO martingales to estimate its contribution to the evolution of the first unknown variable. Then we consider the BSDE having an additive expected value of a quadratic generator in addition to the usual quadratic one. In this case, we use a deterministic shift transformation to the first unknown variable, when the usual quadratic generator depends neither on the first variable nor its mean. The general case can be treated by a fixed point argument.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.