Stability of the split-step backward Euler scheme for stochastic delay integro-differential equations with Markovian switching

2011 ◽  
Vol 16 (2) ◽  
pp. 814-821 ◽  
Author(s):  
Feng Jiang ◽  
Yi Shen ◽  
Junhao Hu
Keyword(s):  
Differential Equations ◽  
Markovian Switching ◽  
Euler Scheme ◽  
Stochastic Delay ◽  
Backward Euler Scheme ◽  
Backward Euler

scholarly journals Estimation of the Hurst index of the solutions of fractional SDE with locally Lipschitz drift

2020 ◽  
Vol 25 (6) ◽  
pp. 1059-1078
Author(s):  
Kęstutis Kubilius
Keyword(s):  
Differential Equations ◽  
Positive Solution ◽  
Euler Scheme ◽  
Hurst Index ◽  
Unique Positive Solution ◽  
Backward Euler Scheme ◽  
Asymptotically Normal ◽  
Backward Euler ◽  
Locally Lipschitz ◽  
Strongly Consistent

Strongly consistent and asymptotically normal estimates of the Hurst index H are obtained for stochastic differential equations (SDEs) that have a unique positive solution. A strongly convergent approximation of the considered SDE solution is constructed using the backward Euler scheme. Moreover, it is proved that the Hurst estimator preserves its properties, if we replace the solution with its approximation.

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>

Split-Step Backward Euler Method for Stochastic Delay Hopfield Neural Networks with Markovian Switching

2011 ◽  
Vol 58-60 ◽  
pp. 1390-1395
Author(s):  
Rong Hua Li ◽  
Li Yang ◽  
Jia Wei Li
Keyword(s):  
Neural Networks ◽  
Euler Method ◽  
Hopfield Neural Networks ◽  
Markovian Switching ◽  
Backward Euler Method ◽  
Approximation Solution ◽  
True Solution ◽  
Stochastic Delay ◽  
Backward Euler ◽  
Exponentially Stable

In this paper, split-step backward Euler method for stochastic delay Hopfield neural networks with Markovian switching is considered. The main aim of this paper is to show that the numerical approximation solution is convergent to the true solution with order. The conditions under which the numerical solution is exponentially stable in mean square are given. An example is provided for illustration.

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