Delay-dependent Asymptotic Stability of Highly Nonlinear Stochastic Differential Delay Equations Driven by G-Brownian Motion. Issue 9 (June 2022)

• Record Type: Journal Article
• Authors: Fei, Chen; Fei, Weiyin; Mao, Xuerong; Yan, Litan
• Is Part Of: Journal of the Franklin Institute. Volume 359:Issue 9(2022)
• Page Start: 4366
• Page End: 4392
• Publication Date: 2022-06
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2022.03.027
• Languages: English
• ISSNs: 0016-0032

Abstract

Abstract: Based on the classical probability, the stability of stochastic differential delay equations (SDDEs) whose coefficients are growing at most linearly has been investigated intensively. Moreover, the delay-dependent stability of highly nonlinear hybrid stochastic differential equations (SDEs) has also been studied recently. In this paper, using the nonlinear expectation theory, we first explore the delay-dependent criteria on the asymptotic stability for a class of highly nonlinear SDDEs driven by G -Brownian motion ( G -SDDEs). Then, the (weak) quasi-sure stability of solutions to G -SDDEs is developed. Finally, an example is analyzed by the φ -max-mean algorithm to illustrate our theoretical results.