| 书目名称 | Random Ordinary Differential Equations and Their Numerical Solution | | 编辑 | Xiaoying Han,Peter E. Kloeden | | 视频video | | | 概述 | Makes recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership.Develops numerical methods for random ODEs | | 丛书名称 | Probability Theory and Stochastic Modelling | | 图书封面 |  | | 描述 | .This book is intended to make recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership, and to familiarize readers with RODEs themselves as well as the closely associated theory of random dynamical systems. In addition, it demonstrates how RODEs are being used in the biological sciences, where non-Gaussian and bounded noise are often more realistic than the Gaussian white noise in stochastic differential equations (SODEs)... .RODEs are used in many important applications and play a fundamental role in the theory of random dynamical systems. They can be analyzed pathwise with deterministic calculus, but require further treatment beyond that of classical ODE theory due to the lack of smoothness in their time variable. Although classical numerical schemes for ODEs can be used pathwise for RODEs, they rarely attain their traditional order since the solutions of RODEs do not have sufficient smoothness to have Taylor expansions in the usual sense. However, Taylor-like expansions can be derived for RODEs using an iterated application of the appropriate chain rule in integral form, and repres | | 出版日期 | Book 2017 | | 关键词 | 37H10, 60H10, 60H35; 34F05, 37H70, 60H30, 65LC30, 65L05, 65L06, 65L20, 92-08; random dynamical systems | | 版次 | 1 | | doi | https://doi.org/10.1007/978-981-10-6265-0 | | isbn_softcover | 978-981-13-4843-3 | | isbn_ebook | 978-981-10-6265-0Series ISSN 2199-3130 Series E-ISSN 2199-3149 | | issn_series | 2199-3130 | | copyright | Springer Nature Singapore Pte Ltd. 2017 |
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发表于 2025-3-21 17:43:14
