McKean–Vlasov过程不变测度的经验近似：平均场相互作用与自相互作用

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-12-28 DOI:10.3150/22-bej1550

Kai Du, Yifan Jiang, Jinfeng Li

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引用次数: 4

摘要

本文证明了在单调性条件下，McKean—Vlasov过程的不变概率测度可以用包括其自身在内的一些过程的加权经验测度来近似。这些过程由分布相关或经验测度相关的随机微分方程描述，该方程由McKean-Vlasov过程的方程构造。经验测度的收敛性以其到不变测度的Wasserstein距离的上界估计为特征。理论结果通过平均场Ornstein-Uhlenbeck过程得到了证明。

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Empirical approximation to invariant measures for McKean–Vlasov processes: Mean-field interaction vs self-interaction

This paper proves that, under a monotonicity condition, the invariant probability measure of a McKean--Vlasov process can be approximated by weighted empirical measures of some processes including itself. These processes are described by distribution dependent or empirical measure dependent stochastic differential equations constructed from the equation for the McKean--Vlasov process. Convergence of empirical measures is characterized by upper bound estimates for their Wasserstein distance to the invariant measure. The theoretical results are demonstrated via a mean-field Ornstein--Uhlenbeck process.

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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.