文章基本信息

标题：Data-Driven Estimation of Infinitesimal Generators of Stochastic Systems ⁎
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作者：Ameneh Nejati ; Abolfazl Lavaei ; Sadegh Soudjani 等
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2021
卷号：54
期号：5
页码：277-282
DOI：10.1016/j.ifacol.2021.08.511
语种：English
出版社：Elsevier
摘要：AbstractThis paper is concerned with a data-driven approach for the estimation of infinitesimal generators of continuous-time stochastic systems with unknown dynamics. We first approximate the infinitesimal generator of the solution process via a set of data collected from trajectories of the unknown system. The approximation utilizes both time discretization and sampling from the solution process. Assuming proper continuity assumptions on dynamics of the system, we then quantify the closeness between the infinitesimal generator and its approximation while providing a priori guaranteed confidence bound. We demonstrate that both the time discretization and the number of data play significant roles in providing a reasonable closeness precision. Moreover, for a fixed size of data, variance of the estimation converges to infinity when the time discretization parameter goes to zero. The formulated error bound shows how to pick proper data size and time discretization jointly to prevent this counter-intuitive behavior. The proposed results are demonstrated on a case study.
关键词：KeywordsContinuous-time stochastic systemsData-driven estimationInfinitesimal generators