The Partially Truncated Euler–Maruyama Method for Highly Nonlinear Stochastic Delay Differential Equations with Markovian Switching

2019 ◽  
Vol 17 (06) ◽  
pp. 1950014 ◽  
Author(s):  
Yuhao Cong ◽  
Weijun Zhan ◽  
Qian Guo
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Markovian Switching ◽  
Variable Delay ◽  
Stochastic Delay Differential Equations ◽  
Type Condition ◽  
Stochastic Delay ◽  
Highly Nonlinear ◽  
Em Method ◽  
Delay Differential

A class of super-linear stochastic delay differential equations (SDDEs) with variable delay and Markovian switching is considered. The main aim of this paper is to investigate the convergence and stability properties of partially truncated Euler–Maruyama (EM) method applied to the SDDEs with variable delay and Markovian switching under the generalized Khasminskii-type condition.

scholarly journals Stability analysis of stochastic delay differential equations with Markovian switching driven by L${\acute{e}}$vy noise

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yanqiang Chang ◽  
Huabin Chen
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Exponential Stability ◽  
Delay Differential Equations ◽  
Existence And Uniqueness ◽  
Markovian Switching ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Delay ◽  
Almost Surely Exponential Stability ◽  
Delay Differential

<p style='text-indent:20px;'>In this paper, the existence and uniquenesss, stability analysis for stochastic delay differential equations with Markovian switching driven by L<inline-formula><tex-math id="M1">\begin{document}$ \acute{e} $\end{document}</tex-math></inline-formula>vy noise are studied. The existence and uniqueness of such equations is simply shown by using the Picard iterative methodology. By using the generalized integral, the Lyapunov-Krasovskii function and the theory of stochastic analysis, the exponential stability in <inline-formula><tex-math id="M2">\begin{document}$ p $\end{document}</tex-math></inline-formula>th(<inline-formula><tex-math id="M3">\begin{document}$ p\geq2 $\end{document}</tex-math></inline-formula>) for stochastic delay differential equations with Markovian switching driven by L<inline-formula><tex-math id="M4">\begin{document}$ \acute{e} $\end{document}</tex-math></inline-formula>vy noise is firstly investigated. The almost surely exponential stability is also applied. Finally, an example is provided to verify our results derived.</p>

scholarly journals A New Stability Criterion for Neutral Stochastic Delay Differential Equations with Markovian Switching

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Wei Hu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Markovian Switching ◽  
Short Paper ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Delay ◽  
Diffusion Operator ◽  
Analysis Technique ◽  
Delay Differential ◽  
Moment Exponential Stability

In this short paper, a new stability theorem for neutral stochastic delay differential equations with Markovian switching is investigated by applying stochastic analysis technique and Razumikhin stability approach. A novel criterion of the pth moment exponential stability is derived for the related systems. The feature of the criterion shows that the estimated upper bound for the diffusion operator of Lyapunov function is allowed to be indefinite, even if to be unbounded, which can loosen the constraints of the existing results. Last, an example is provided to illustrate the usefulness and significance of the theoretical results.

scholarly journals Asymptotic stability of the time-changed stochastic delay differential equations with Markovian switching

2021 ◽  
Vol 19 (1) ◽  
pp. 614-628
Author(s):  
Xiaozhi Zhang ◽  
Zhangsheng Zhu ◽  
Chenggui Yuan
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Markovian Switching ◽  
Stability Of Solutions ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Delay ◽  
The Stability ◽  
Delay Differential

Abstract The aim of this work is to study the asymptotic stability of the time-changed stochastic delay differential equations (SDDEs) with Markovian switching. Some sufficient conditions for the asymptotic stability of solutions to the time-changed SDDEs are presented. In contrast to the asymptotic stability in existing articles, we present the new results on the stability of solutions to time-changed SDDEs, which is driven by time-changed Brownian motion. Finally, an example is given to demonstrate the effectiveness of the main results.

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