Approximation of a class of functional differential equations with wideband noise perturbations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:496

Article

Wu, Fuke¹  Yin, George²  Zhu, Chao³ 

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China

[2] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

[3] Univ Wisconsin, Dept Math Sci, Milwaukee, WI 53201 USA

关键词: Wideband noise;    Functional derivative;    Stochastic functional differential equation;    Weak convergence;    Martingale method;   

DOI  :  10.1016/j.jmaa.2020.124819

来源: Elsevier

【 摘 要 】

This work focuses on functional differential equations subject to wideband noise perturbations. Modeling using a white noise is often an idealization of the actual physical process, whereas a wideband noise can be easily realized in applications and well approximates a white noise. Using functional derivatives together with the combined perturbed test function methods and martingale techniques, this paper demonstrates that when a small parameter tends to zero, the underlying process converges to a limit that is the solution of a stochastic functional differential equation. To illustrate, an integro-differential system with wideband noise perturbation is examined as an example. Not only are the results interesting from a mathematical point of view, but also they are of utility to a wide range of applications. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free