渐增上鞅耦合的基于势的构造

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-01 DOI:10.1214/22-aap1907

Erhan Bayraktar, Shuoqing Deng, Dominykas Norgilas

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引用次数: 4

摘要

由Nutz和Stebegg (Ann)提出的渐增的上鞅耦合。Probab. 46(2018) 3351-3398)是两个实概率测度之间以凸递减顺序的“上鞅”耦合集的极值点。在本文中，我们给出了一个三重函数的显式构造，其上鞅耦合集中在图上。特别地，我们证明了增加的上鞅耦合可以分别识别为一个唯一确定的状态切换点的左幕鞅耦合和左、右对调耦合。我们的建筑是基于阴影测量的概念。我们展示了如何确定与上鞅相关的阴影测量的潜力，扩展了Beiglböck等人的最新结果。Commun。概率27(2022)1-12)在鞅设置中获得。

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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A potential-based construction of the increasing supermartingale coupling

The increasing supermartingale coupling, introduced by Nutz and Stebegg (Ann. Probab. 46 (2018) 3351–3398) is an extreme point of the set of “supermartingale” couplings between two real probability measures in convex-decreasing order. In the present paper we provide an explicit construction of a triple of functions, on the graph of which the increasing supermartingale coupling concentrates. In particular, we show that the increasing supermartingale coupling can be identified with the left-curtain martingale coupling and the antitone coupling to the left and to the right of a uniquely determined regime-switching point, respectively. Our construction is based on the concept of the shadow measure. We show how to determine the potential of the shadow measure associated to a supermartingale, extending the recent results of Beiglböck et al. (Electron. Commun. Probab. 27 (2022) 1–12) obtained in the martingale setting.

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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.