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

IF 1 Q3 Engineering

Journal of Computational Dynamics 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.

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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。

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来源期刊

Journal of Computational Dynamics Engineering-Computational Mechanics

CiteScore

2.30

自引率

10.00%

发文量

期刊介绍： JCD is focused on the intersection of computation with deterministic and stochastic dynamics. The mission of the journal is to publish papers that explore new computational methods for analyzing dynamic problems or use novel dynamical methods to improve computation. The subject matter of JCD includes both fundamental mathematical contributions and applications to problems from science and engineering. A non-exhaustive list of topics includes * Computation of phase-space structures and bifurcations * Multi-time-scale methods * Structure-preserving integration * Nonlinear and stochastic model reduction * Set-valued numerical techniques * Network and distributed dynamics JCD includes both original research and survey papers that give a detailed and illuminating treatment of an important area of current interest. The editorial board of JCD consists of world-leading researchers from mathematics, engineering, and science, all of whom are experts in both computational methods and the theory of dynamical systems.