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Keywords = quasi-sure exponential stability

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18 pages, 308 KB  
Article
Quasi-Sure Exponential Stability of Stochastic Differential Delay Systems Driven by G-Brownian Motion
by Chen Fei, Luzhen Yang and Weiyin Fei
Symmetry 2025, 17(2), 214; https://doi.org/10.3390/sym17020214 - 31 Jan 2025
Viewed by 867
Abstract
This paper focuses on the quasi-sure exponential stability of the stochastic differential delay equation driven by G-Brownian motion (SDDE-GBM): [...] Read more.
This paper focuses on the quasi-sure exponential stability of the stochastic differential delay equation driven by G-Brownian motion (SDDE-GBM): dξ(t)=f(t,ξ(tκ1(t)))dt+g(t,ξ(tκ2(t)))dZ(t), where κ1(·),κ2(·):R+[0,τ] denote variable delays, and Z(t) denotes scalar G-Brownian motion, which has a symmetry distribution. It is shown that the SDDE-GBM is quasi-surely exponentially stable for each τ>0 bounded by τ*, where the corresponding (non-delay) stochastic differential equation driven by G-Bronwian motion (SDE-GBM), dη(t)=f(t,η(t))dt+g(t,η(t))dZ(t), is quasi-surely exponentially stable. Moreover, by solving the non-linear equation on τ, we can obtain the implicit lower bound τ*. Finally, illustrating examples are provided. Full article
(This article belongs to the Special Issue Symmetric or Asymmetric Distributions and Its Applications)
16 pages, 328 KB  
Article
Impulsive Stability of Stochastic Functional Differential Systems Driven by G-Brownian Motion
by Lijun Pan, Jinde Cao and Yong Ren
Mathematics 2020, 8(2), 227; https://doi.org/10.3390/math8020227 - 10 Feb 2020
Cited by 7 | Viewed by 2154
Abstract
This paper is concerned with the p-th moment exponential stability and quasi sure exponential stability of impulsive stochastic functional differential systems driven by G-Brownian motion (IGSFDSs). By using G-Lyapunov method, several stability theorems of IGSFDSs are obtained. These new results are employed [...] Read more.
This paper is concerned with the p-th moment exponential stability and quasi sure exponential stability of impulsive stochastic functional differential systems driven by G-Brownian motion (IGSFDSs). By using G-Lyapunov method, several stability theorems of IGSFDSs are obtained. These new results are employed to impulsive stochastic delayed differential systems driven by G-motion (IGSDDEs). In addition, delay-dependent method is developed to investigate the stability of IGSDDSs by constructing the G-Lyapunov–Krasovkii functional. Finally, an example is given to demonstrate the effectiveness of the obtained results. Full article
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