The stability with general decay rate of neutral stochastic functional hybrid differential equations with Lévy noise

2020 ◽  
Vol 143 ◽  
pp. 104742
Author(s):  
Guangjun Shen ◽  
Wentao Xu ◽  
Dongjin Zhu
Keyword(s):  
Differential Equations ◽  
Decay Rate ◽  
General Decay ◽  
Lévy Noise ◽  
General Decay Rate ◽  
The Stability ◽  
Levy Noise ◽  
Hybrid Differential Equations ◽  
Stochastic Functional

scholarly journals General Decay Stability for Stochastic Functional Differential Equations with Infinite Delay

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Yue Liu ◽  
Xuejing Meng ◽  
Fuke Wu
Keyword(s):  
Differential Equations ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
General Decay ◽  
Stochastic Functional Differential Equations ◽  
General Decay Rate ◽  
Polynomial Coefficients ◽  
Functional Differential ◽  
The Stability ◽  
Stochastic Functional

So far there are not many results on the stability for stochastic functional differential equations with infinite delay. The main aim of this paper is to establish some new criteria on the stability with general decay rate for stochastic functional differential equations with infinite delay. To illustrate the applications of our theories clearly, this paper also examines a scalar infinite delay stochastic functional differential equations with polynomial coefficients.

scholarly journals Stability with general decay rate of hybrid neutral stochastic pantograph differential equations driven by Lévy noise

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Tian Zhang ◽  
Chuanhou Gao
Keyword(s):  
Differential Equations ◽  
Decay Rate ◽  
Broad Class ◽  
General Decay ◽  
Polynomial Decay ◽  
Almost Sure Stability ◽  
General Decay Rate ◽  
Varying Coefficients ◽  
Highly Nonlinear ◽  
Time Varying Coefficients

<p style='text-indent:20px;'>This paper focuses on the <inline-formula><tex-math id="M2">\begin{document}$ p $\end{document}</tex-math></inline-formula>th moment and almost sure stability with general decay rate (including exponential decay, polynomial decay, and logarithmic decay) of highly nonlinear hybrid neutral stochastic pantograph differential equations driven by L<inline-formula><tex-math id="M3">\begin{document}$ \acute{e} $\end{document}</tex-math></inline-formula>vy noise (NSPDEs-LN). The crucial techniques used are the Lyapunov functions and the nonnegative semi-martingale convergence theorem. Simultaneously, the diffusion operators are permitted to be controlled by several additional functions with time-varying coefficients, which can be applied to a broad class of the non-autonomous hybrid NSPDEs-LN with highly nonlinear coefficients. Besides, <inline-formula><tex-math id="M4">\begin{document}$ H_\infty $\end{document}</tex-math></inline-formula> stability and the almost sure asymptotic stability are also concerned. Finally, two examples are offered to illustrate the validity of the obtained theory.</p>

scholarly journals Mean square stability with general decay rate of nonlinear neutral stochastic function differential equations in the $ G $-framework

2022 ◽  
Vol 7 (4) ◽  
pp. 5752-5767
Author(s):  
Guangjie Li ◽  
Keyword(s):  
Differential Equations ◽  
Decay Rate ◽  
Trivial Solution ◽  
General Decay ◽  
Mean Square ◽  
General Decay Rate ◽  
Diffusion Operator ◽  
Mean Square Stability ◽  
Stochastic Function ◽  
Exponentially Stable

<abstract><p>Few results seem to be known about the stability with general decay rate of nonlinear neutral stochastic function differential equations driven by $ G $-Brownain motion ($ G $-NSFDEs in short). This paper focuses on the $ G $-NSFDEs, and the coefficients of these considered $ G $-NSFDEs can be allowed to be nonlinear. It is first proved the existence and uniqueness of the global solution of a $ G $-NSFDE. It is then obtained the trivial solution of the $ G $-NSFDE is mean square stable with general decay rate (including the trivial solution of the $ G $-NSFDE is mean square exponentially stable and the trivial solution of the $ G $-NSFDE is mean square polynomially stable) by $ G $-Lyapunov functions technique. In this paper, auxiliary functions are used to dominate the Lyapunov function and the diffusion operator. Finally, an example is presented to illustrate the obtained theory.</p></abstract>

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