Extracting non-Gaussian governing laws from data on mean exit time

Yanxia Zhang, Jinqiao Duan, Yanfei Jin*, Yang Li

*此作品的通讯作者

科研成果: 期刊稿件文章同行评审

13 引用 (Scopus)

摘要

Motivated by the existing difficulties in establishing mathematical models and in observing state time series for some complex systems, especially for those driven by non-Gaussian Lévy motion, we devise a method for extracting non-Gaussian governing laws with observations only on the mean exit time. It is feasible to observe the mean exit time for certain complex systems. With such observations, we use a sparse regression technique in the least squares sense to obtain the approximated function expression of the mean exit time. Then, we learn the generator and further identify the governing stochastic differential equation by solving an inverse problem for a nonlocal partial differential equation and minimizing an error objective function. Finally, we verify the efficacy of the proposed method by three examples with the aid of the simulated data from the original systems. Results show that our method can apply to not only the stochastic dynamical systems driven by Gaussian Brownian motion but also those driven by non-Gaussian Lévy motion, including those systems with complex rational drift.

源语言英语
文章编号113112
期刊Chaos
30
11
DOI
出版状态已出版 - 1 11月 2020

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