Conditioned Wiener processes as nonlinearities: A rigorous probabilistic analysis of dynamics

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-09-23 DOI:10.3934/jcd.2023004

K. Mischaikow, Cameron Thieme

引用次数: 0

Abstract

We study a Weiner process that is conditioned to pass through a finite set of points and consider the dynamics generated by iterating a sample path from this process. Using topological techniques we are able to characterize the global dynamics and deduce the existence, structure and approximate location of invariant sets. Most importantly, we compute the probability that this characterization is correct. This work is probabilistic in nature and intended to provide a theoretical foundation for the statistical analysis of dynamical systems which can only be queried via finite samples.

查看原文本刊更多论文

作为非线性的条件维纳过程:动力学的严格概率分析

我们研究了一个Weiner过程，它被限定为通过有限的点集，并考虑了从这个过程中迭代样本路径所产生的动力学。利用拓扑技术，我们能够描述全局动力学，并推导出不变量集的存在性、结构和近似位置。最重要的是，我们计算了这种描述是正确的概率。这项工作本质上是概率性的，旨在为只能通过有限样本查询的动力系统的统计分析提供理论基础。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.